Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova...

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Methods of Analysis for Nested Petri Nets (NP-nets) Preface Prerequisites of NP-nets Simple model of P2P protocol Definition of Nested Petri Net (NP-net) Need for analysis methods Compositionality of NP-net properties Technical achievements Ongoing research Conclusions 1.1 Methods of Analysis for Nested Petri Nets (NP-nets) p1 p2 p3 p4 p5 p6 p7 t1 β x x t2 β x x t3 τ z z t4 λ z z t5 τ z z t6 λ z z p8 p9 t7 λ t8 β t9 β t10 λ p8 p9 t7 λ t8 β t9 β t10 λ SN: α1: α2: Speaker: L. Dworzanski ([email protected]) Sci. Advisor: I. A. Lomazova ([email protected]) National Research University Higher School of Economics

Transcript of Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova...

Page 1: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.1

Methods of Analysis forNested Petri Nets (NP-nets)

p1 p2

p3

p4 p5 p6 p7

t1 β

x x

t2 βxx

t3 τ

z

z

t4 λ

z

z

t5 τ

z

z

t6 λ

z

z

p8 p9

t7 λ

t8

β

t9

β

t10 λ

p8 p9

t7 λ

t8

β

t9

β

t10 λ

SN :

α1: α2:

Speaker: L. Dworzanski ([email protected])Sci. Advisor: I. A. Lomazova ([email protected])

National Research University Higher School of Economics

Page 2: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.2

NP-nets — the first impressionAn instance of “nets-within-nets” paradigm (cf. R.Valk 1998)

p1 p2

p3

p4 p5 p6 p7

t1 β

x x

t2 βxx

t3 τ

z

z

t4 λ

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t7 λ

t8

β

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β

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p8 p9

t7 λ

t8

β

t9

β

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SN :

α1: α2:

Figure : An NP-net — a caught sample.

Page 3: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.3

Whats the Plan?

• Prerequisites of NP-nets• Ostensive definition of NP-nets: Simple model of P2P

protocol• Formal definition of NP-nets• Need for analysis methods• Compositionality of NP-net properties• Technical achievements• Ongoing research• Conclusions and further directions

Page 4: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.4

Prerequisites of NP-nets

• Via NP-nets we can model/execute adaptive workflow netsand handle exceptions. For details:K. M. van Hee, I. A. Lomazova, O. Oanea, A. Serebrenik,N. Sidorova, M. Voorhoeve: Nested Nets for AdaptiveSystems. ICATPN 2006: 241-260

• “Flat” Petri nets is an inconvenient tool to model systemswith distributed agents

• P2P protocols: system net (SN) — orchestration protocol,tokens — peers with protocols implementations (cf. L.Dworzanski, I.A.Lomazova, PSSV’11);

• Wireless sensor networks: SN — physical topology andorchestration protocol, tokens — sensors (cf. N. Buchinapaper);

• Social systems: SN — software process, tokens — stuff(developers, testers, project managers et cetera) (A.Phillipov model).

• Swarm systems: SN — orchestration protocol, tokens —attacking drones (D. Frumin model),

• other applications: unix daemons, mobile code, mobilerobot system etc.

Page 5: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.5

Whats the Plan?

• Prerequisites of NP-nets• Ostensive definition of NP-nets: Simple model of P2P

protocol• Formal definition of NP-nets• Need for analysis methods• Compositionality of NP-net properties• Technical achievements• Ongoing research• Conclusions and further directions

Page 6: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.6

Case study: P2P protocol

P2P protocol (system) consists of the participants of threekinds

• Seeds — sources of datum;• Peers — consumers of datum;• Tracking server — coordinator of seeds and peers

interaction.

Page 7: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.7

Seed

A seed is a source of data. In the initial state it waits for arequest from a peer to upload the data to the peer. Then itclears its upload buffer and returns to the initial state.

p1

p2

p3t1

λ

t2

λ

t3

λ

E1(seed):

Figure : Seed net.

Page 8: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.8

Peer

A peer is just a consumer of data. In the initial state it waits fora seed with a piece of datum. Then it downloads the data andreturns to the initial state.

p4 p5t4

λ

t5

λ

E2(peer):

Figure : Peer net.

Page 9: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.9

Tracking server

A tracking server is a coordinator of the seeds and peersinteraction. It has the pools for ready-to-transmit peers andseeds and the pool for reinitializing seeds.

p16

p17

p19

p20

p22

t14 λ

x

y x

y

t15 λx

x

t16 λ

x

y

x

y

SN(protocol):

Figure : Tracking server.

Page 10: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.10

PipeTracking server coordinates such interactions by introducing anew entity — pipe. In the initial state a pipe waits for a seedand a peer, then it coordinates their interaction. Then the pipereinitializates its internal buffers and returns to the initial state.A pipe can handle such aspects of a transmition as security,reliability, anonimousity etc.

p6

p7

p8

p9

p10

p11 p12

p13

p14 p15

t6

t7 t8 t9

t10λ

t11 λ

t12λ

E3(pipe):

Figure : Pipe net.

Page 11: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.11

Tracking server

Returning to our tracking server. There are no pipes.

p16

p17

p19

p20

p22

t14 λ

x

y x

y

t15 λx

x

t16 λ

x

y

x

y

SN(protocol):

Figure : Tracking server.

Page 12: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.12

Tracking server

But we can add them.

p16

p17

p18

p19

p20

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p22

p23

t14 λ

x

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t15 λy

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t16 λ

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t17 λ

z

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SN(protocol):

Figure : Tracking server.

Page 13: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.13

The whole picture

p1

p2

p3t1

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t2

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p4 p5t4

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p6

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p11 p12

p13

p14 p15

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t12λ

p16

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 14: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.14

NP-net

p1

p2

p3t1

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t2

λ

t3

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t5

λ

p6

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p13

p14 p15

t6

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t12λ

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 15: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.15

NP-net

p1

p2

p3t1

λ

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λ

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p7

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p13

p14 p15

t6

t7 t8 t9

t10λ

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t12λ

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p17

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t17 λ

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 16: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.16

NP-net

p1

p2

p3t1

λ

t2

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p13

p14 p15

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t12λ

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t14 λ

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t17 λ

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 17: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.17

NP-net

p1

p2

p3t1

λ

t2

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λ

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λ

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p7

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p13

p14 p15

t6

t7 t8 t9

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t12λ

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 18: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.18

NP-net

p1

p2

p3t1

λ

t2

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t3

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λ

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p13

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t12λ

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p20

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 19: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.19

NP-net

p1

p2

p3t1

λ

t2

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p13

p14 p15

t6

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 20: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.20

NP-net

p1

p2

p3t1

λ

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λ

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t11 λ

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 21: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.21

NP-net

p1

p2

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p4 p5t4

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p11 p12

p13

p14 p15

t6

t7 t8 t9

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t12λ

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E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 22: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.22

NP-net: net constants, net token elimination

p1

p2

p3

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t

λx+ z

y

2 · x

c+ y

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p2

p3

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t

λx+ z

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2 · x

c+ y

p5 p6t1

λ

p5 p6t1

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p5 p6t1

λ

p5 p6t1

λ

p7 p8t2

λ

p7 p8t2

λ

p7 p8t2

λ

m: m′:

α1: α11:α12:

α2: α′2:

αc:

α3:

Page 23: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.23

Whats the Plan?

• Prerequisites of NP-nets• Ostensive definition of NP-nets: Simple model of P2P

protocol• Formal definition of NP-nets• Need for analysis methods• Compositionality of NP-net properties• Technical achievements• Ongoing research• Conclusions and further directions

Page 24: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.24

NP-net

Definition

Two-level NP-net is a tupleNP = 〈Lab,SN,E〉 where

• Lab — set of labels for synchronization of transitions;• SN — system net of the NP-net;• E – finite set of element nets.

Page 25: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.25

NP-net

Definition

System net is a tupleSN = 〈N,L,U ,W ,m0〉 where

• N = 〈PSN ,TSN ,FSN〉 — high-level PN of System net;• PSN — set of typed places;• L = Expr — arc expression language

(sums of constants and variables);• U = 〈A, I〉 — model of L with domain A = Anet ∪ Aatom;• Anet – set of marked element nets (net tokens);• Aatom — set of plain colored tokens;• I : Con → A — interpretation function;• W : FSN → L — arc expression function;• Λ : TSN → Lab — transition labeling function.

Page 26: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.26

Restrictions

1 constants or multiple instances of the same variable arenot allowed in input arc expressions of t ;

2 each variable in an output arc expression for t occurs inone of the input arc expressions of t .

Page 27: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.27

Whats the Plan?

• Prerequisites of NP-nets• Ostensive definition of NP-nets: Simple model of P2P

protocol• Formal definition of NP-nets• Need for analysis methods• Compositionality of NP-net properties• Technical achievements• Ongoing research• Conclusions and further directions

Page 28: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.28

Need for analysis methods

Common sense:

• Vertical synchronization, additional levels, net tokenscreation and destruction, net tokens constants;

• Distributed concurrent systems are complex andnon-tractable for human understanding;

• Distributed concurrent systems with dynamical hierarchicalstructure are even more complex;

Page 29: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.29

Need for analysis methods

Theoretical issues:

• Covering problem is decidable

• NP-nets strictly more expressive than Petri nets• It is possible to model Petri nets w/ reset arcs via NP-nets

so...• Boundedness is undecidable• Reachability is undecidable• Liveness is undecidable

What can we do?

Page 30: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.29

Need for analysis methods

Theoretical issues:

• Covering problem is decidable• NP-nets strictly more expressive than Petri nets• It is possible to model Petri nets w/ reset arcs via NP-nets

so...

• Boundedness is undecidable• Reachability is undecidable• Liveness is undecidable

What can we do?

Page 31: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.29

Need for analysis methods

Theoretical issues:

• Covering problem is decidable• NP-nets strictly more expressive than Petri nets• It is possible to model Petri nets w/ reset arcs via NP-nets

so...• Boundedness is undecidable• Reachability is undecidable• Liveness is undecidable

What can we do?

Page 32: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.29

Need for analysis methods

Theoretical issues:

• Covering problem is decidable• NP-nets strictly more expressive than Petri nets• It is possible to model Petri nets w/ reset arcs via NP-nets

so...• Boundedness is undecidable• Reachability is undecidable• Liveness is undecidable

What can we do?

Page 33: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.30

Whats the Plan?

• Prerequisites of NP-nets• Ostensive definition of NP-nets: Simple model of P2P

protocol• Formal definition of NP-nets• Need for analysis methods• Compositionality of NP-net properties• Technical achievements• Ongoing research• Conclusions and further directions

Page 34: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.31

Compositionality and modularity

Modularity allows

• describe system’s components independently.

Compositionality enables• derive system properties from properties of its

components;• reuse components’ analysis results for systems with same

components (library of verified components);

Page 35: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.32

Compositionality and modularity

Prof. Joseph Sifakis, A Dialogue with Professor Joseph Sifakisabout Concurrent Systems Specification and Verification,Bulletin of the European Association for Theoretical ComputerScience, 104, 2011We need theory, models and tools for cost-effectivelybuilding complex systems by assembling heterogeneouscomponents

• As system synthesis from requirements is intractable forcomplex systems, we should study principles for buildingcorrect systems from components. The aim is to avoid aposteriori monolithic verification as much as possible;

Page 36: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.33

Compositionality and modularity

Prof. Joseph Sifakis, A Dialogue with Professor Joseph Sifakisabout Concurrent Systems Specification and Verification(contd.),

• (Complexity problem) As system synthesis fromrequirements is intractable for complex systems, weshould study principles for building correct systems fromcomponents. The aim is to avoid a posteriori monolithicverification as much as possible;

• (Constructive correctness) How can the global propertiesof a composite system be effectively inferred from theproperties of its constituents? This remains an old openproblem that urgently needs answers.

• Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-freecomponents is - under some conditions - a deadlock-freecomponent;

Page 37: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.33

Compositionality and modularity

Prof. Joseph Sifakis, A Dialogue with Professor Joseph Sifakisabout Concurrent Systems Specification and Verification(contd.),

• (Complexity problem) As system synthesis fromrequirements is intractable for complex systems, weshould study principles for building correct systems fromcomponents. The aim is to avoid a posteriori monolithicverification as much as possible;

• (Constructive correctness) How can the global propertiesof a composite system be effectively inferred from theproperties of its constituents? This remains an old openproblem that urgently needs answers.

• Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-freecomponents is - under some conditions - a deadlock-freecomponent;

Page 38: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.33

Compositionality and modularity

Prof. Joseph Sifakis, A Dialogue with Professor Joseph Sifakisabout Concurrent Systems Specification and Verification(contd.),

• (Complexity problem) As system synthesis fromrequirements is intractable for complex systems, weshould study principles for building correct systems fromcomponents. The aim is to avoid a posteriori monolithicverification as much as possible;

• (Constructive correctness) How can the global propertiesof a composite system be effectively inferred from theproperties of its constituents? This remains an old openproblem that urgently needs answers.

• Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-freecomponents is - under some conditions - a deadlock-freecomponent;

Page 39: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.34

Compositionality and modularity

p1 p2

p3

p4 p5 p6 p7

t1 β

x x

t2 βxx

t3 τ

z

z

t4 λ

z

z

t5 τ

z

z

t6 λ

z

z

p8 p9

t7 λ

t8

β

t9

β

t10 λ

p8 p9

t7 λ

t8

β

t9

β

t10 λ

SN :

α1: α2:

Page 40: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.35

Compositionality and modularity

Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-free componentsis - under some conditions - a deadlock-free component.

For a given NP-net N:• The element nets of N are classical Petri nets;

• The net-tokens and net constants of N are instances ofthe element nets;

• The system net of N can be considered as classical PN, ifwe abstract from internal contents of net-tokens;

• The whole NP-net N can be considered as thecomposition of the system net and the element nets.

Page 41: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.35

Compositionality and modularity

Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-free componentsis - under some conditions - a deadlock-free component.

For a given NP-net N:• The element nets of N are classical Petri nets;• The net-tokens and net constants of N are instances of

the element nets;

• The system net of N can be considered as classical PN, ifwe abstract from internal contents of net-tokens;

• The whole NP-net N can be considered as thecomposition of the system net and the element nets.

Page 42: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.35

Compositionality and modularity

Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-free componentsis - under some conditions - a deadlock-free component.

For a given NP-net N:• The element nets of N are classical Petri nets;• The net-tokens and net constants of N are instances of

the element nets;• The system net of N can be considered as classical PN, if

we abstract from internal contents of net-tokens;

• The whole NP-net N can be considered as thecomposition of the system net and the element nets.

Page 43: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.35

Compositionality and modularity

Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-free componentsis - under some conditions - a deadlock-free component.

For a given NP-net N:• The element nets of N are classical Petri nets;• The net-tokens and net constants of N are instances of

the element nets;• The system net of N can be considered as classical PN, if

we abstract from internal contents of net-tokens;• The whole NP-net N can be considered as the

composition of the system net and the element nets.

Page 44: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.36

Compositionality and modularity

Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-free componentsis - under some conditions - a deadlock-free component.

For a given NP-net N:• The components of N satisfy some property;

• Some structural/behavioural conditions are satisfied• The whole NP-net N satisfies some property.

Page 45: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.36

Compositionality and modularity

Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-free componentsis - under some conditions - a deadlock-free component.

For a given NP-net N:• The components of N satisfy some property;• Some structural/behavioural conditions are satisfied

• The whole NP-net N satisfies some property.

Page 46: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.36

Compositionality and modularity

Compositionality rules for inferring global properties ofcomposite components from the properties of constituentcomponents e.g. the composition of deadlock-free componentsis - under some conditions - a deadlock-free component.

For a given NP-net N:• The components of N satisfy some property;• Some structural/behavioural conditions are satisfied• The whole NP-net N satisfies some property.

Page 47: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.37

Compositionality and modularity

p1 p2

p3

p4 p5 p6 p7

t1 β

x x

t2 βxx

t3 τ

z

z

t4 λ

z

z

t5 τ

z

z

t6 λ

z

z

p8 p9

t7 λ

t8

β

t9

β

t10 λ

p8 p9

t7 λ

t8

β

t9

β

t10 λ

SN :

α1: α2:

Page 48: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.38

Boundedness compositionality

Definition

Marked NP-net NP is bounded iff its reachability set RNP(m0)is finite.

Theorem

Let NP be a marked NP-net. If1 the system net in NP is bounded (as a separate

component, i.e. a flat PN)2 all net tokens in the initial marking are bounded (as

separate components)3 all net constants in arc expressions in NP are bounded (as

separate components)then NP is bounded.

Page 49: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.39

Counterexamples for boundedness (1)

p3t2

τ

p1 p2t1

τx

xxα1

α1:

SN:

Condition: “the system net in NP is bounded”

p2 p3t2

τ

p1t1

τx

xα1

α1:

SN:

Condition: “all net tokens in the initial marking are bounded”

Page 50: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.40

Counterexamples for boundedness (2)

p2 p3t2

τ

p1 p4t1

τα1 α1

α1:

SN:

Condition: all net constants in arc expressions are bounded”

Page 51: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.41

Single label case: Liveness compositionality (0L-live)

Definition

Let NP be a marked two-level NP-net. NP is called 0L-live iffevery transition in its system net is live.

Theorem

Let NP be a marked two-level NP-net. Let also NP satisfy thefollowing conditions:

1 the system net in NP is live (as a separate component, i.e.a flat PN);

2 all net tokens in the initial marking and all net constants inevery arc expression are live (as separate components);

3 NP has only one label of vertical synchronization λ;4 if t is a system net transition in NP labeled with λ, then for

any p ∈ •t the type of p is an element net, containing atransition labeled with λ.

Then NP is 0L-live.

1,2 — counterexamples are similiar to boundedness property,3,4 — counterexamples are given below

Page 52: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.42

Counterexamples for 0L-liveness (1)

p3 p4

t3

λa

t4

λb

p1 p2

t1

λb

t2

λa

α1

α1:

SN:

Condition: “NP has only one label of vertical synchronizationλ”.

Page 53: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.43

Counterexamples for 0L-liveness (2)

p3 p4

τ

τ

p1 p2 p5

τ

τ

τ

λ

α1

α1:

SN:

Condition: “if t is a system net transition labeled with λ, then forany p ∈ •t the type of p is an element net, containing atransition labeled with λ”.

Page 54: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.44

Single label case: Liveness compositionality (1L-live) (1)

Definition

Let NP be a marked NP-net. NP is said to be 1L-live iff everytransition of its system net and every transition in each nettoken from the initial marking in NP are live.

Theorem

Let NP be a marked NP-net.1 the system net in NP is live (as a separate component);2 all net tokens in the initial marking and all net constants in

every arc expression are live (as separate components);3 NP has only one label for vertical synchronization λ;4 if t is a system net transition in NP labeled by λ, then for

any p ∈ •t an element net corresponding to p contains atransition labeled with λ;

5 NP is conservative (on the next slide)6 each SCC of the system net contains at least one

transition labeled with λ.Then NP is 1L-live.

Page 55: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.45

Conservative NP-nets

Definition

Let NP be an NP-net. NP is called conservative iff for eachtransition t in the system net of NP the set of all variables in theinput arc expressions for t is a subset of all variables in itsoutput arc expressions.

Conservativeness is needed as for 1L-liveness we considerliveness of net-tokens. In exiled net-tokens transitions are“dead”:

p3 p4

τ

τ

p1 p2

τx x

τ

xα1

α

E1: SN:

However, if we don’t bother about eliminated net-tokens, wecan exclude the condition about convervativeness.

Page 56: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.46

Counterexamples for 1L-liveness (1)

p3 p4

λ

τ

p1 p2 p3

p4

τx x

λ

xx

τx xτ

x

x

τx

x

α1

α1:

SN:

Condition: each SCC of the system net contains at least onetransition labeled with λ.Note: SCCs in SN are cycles in α-trail nets (defined below)

Page 57: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.47

Multiple labels case: Liveness compositionality (1L-live) (1)

Theorem

Let NP be a conservative marked NP-net with a system net SNand initial marking m0. Let also NP satisfy the followingconditions:

1 the system net in NP is live (as a separate component);2 all net tokens in the initial marking m0 and all net constants

in all arc expression in SN are live (as separatecomponents);

3 for each net token α in m0: α is m-bisimilar to the α-trailnet for NP;

4 for each arc (t ,p) with arc expression e in SN: if econtains a net constant with a value α, then α ism-bisimular to the α-trail net for NP with the initial markingmα, where mα(p) = α, i.e. α resides in p.

Then NP is 1L-live.

Page 58: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.48

α-trail net extraction (1)

How to construct α-trail net for the position pα of the systemnet SN of an NP-net:

Definition

Step 0. We start building the α-trail net with a new placep′, corresponding to pα, and consider pα as acurrent place in SN.

Step 1. Let p be a current place, and let t be a transitionin SN, for which p is an income place, i.e. thereis an arc from p to t with an arc expression expr .Let V be the set of variables occurring in expr .For each v ∈ V, s.t. there is an arc from t tosome place with an expression containing v , webuild a new transition t ′ and a new place p′:•t ′ = p, t ′• = p′ and λ(t ′) = λ(t).

Step 2. Repeat Step 1 with every new place as a currentplace.

Illustrations are on the next slide.

Page 59: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.49

α-trail net extraction (2)

p1

p2

p3

p4

t

λx + y

x + y

y p1

p2

p4

t ′

λ

t ′′

λ

SN: α-trail net:

• path p1 → t ′ → p2 — is a trajectory of a net token under xor y variables from x + y expression on the arc 〈t ,p2〉.

• path p1 → t ′′ → p4 — is a trajectory of a net token under yvariable from the arc 〈t ,p4〉

No net token can traverse through the t-p3 arc, so there is nocorresponding arc in the constructed α-trail net.

Page 60: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.50

α-trail net extraction (3)

p1

p2

p3

p4

p5

p6

t1

ax

y

x

y

t2

bx

y

x

y

t3

cxx

x

t4

d xx

p1 p3

p4

p5

p6

t ′1

a

t ′2

b

t ′3

c

t ′′3

c

t ′4d

t ′′2b

α

SN:

α-trail net:

Here is a more complex case of α-trail net extraction.

Page 61: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.51

α-trail net extraction (4)

α-trail net extraction is just a specialization of an extraction ofNDA from high level Petri net with transitive inclusion of a tokenplace propagation.

Page 62: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.52

1L-liveness for several labels NP-nets

p11 p12

p13

p14 p15

τ

ττ

λa

λa

λc

τ

p1

p2 p3

p4 p5

λa

x

x

λa

x

x

λc

x x

λb

x x

τ xx

τ x

xα1

α1:

SN:

This NP-net has infinite executions, but it’s not 1L-live, due tobreak of m-bisimulation.

Page 63: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.53

Properties of the components

All components are• free-choice (syntactically)• bounded• live

For Seed and Peer nets this is trivial

p1

p2

p3t1

λ

t2

λ

t3

λ

E1(seed):

p4 p5t4

λ

t5

λ

E2(peer):

Page 64: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.54

Properties of the components

For protocol net (System Net)

p16

p17

p18

p19

p20

p21

p22

p23

t14 λ

x

y

z

x

y

z

t15 λy

y

t16 λ

x

y

z

x

y

z

t17 λ

z

z

SN(protocol):

• Free-choiceness — syntactically• Boundedness — as preset and postset powers are equal

for each transition• Liveness — by simple T-invariant 〈1,1,1,1〉

(transitions are enumerated by their index)

Page 65: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.55

Properties of the components

For Pipe net (E3)

p6

p7

p8

p9

p10

p11 p12

p13

p14 p15

t6

t7 t8 t9

t10λ

t11 λ

t12λ

E3(pipe):

• Free-choice — syntactically• Boundedness — by simple S-invariant〈1,1,1,1,1,1,1,1,2,2〉(places are enumerated by their index)

• Liveness — by simple T-invariant 〈1,1,1,1,1,1,1〉Invariants are simple as we artificially constructed our exampleto be simple.

Page 66: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.56

Properties of the system

We can conclude the next properties of the whole system• Boundedness — as “boundedness compositionality”

conditions hold;• “1L-live” property — as “1L-live” conditions hold.

Page 67: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.57

Whats the Plan?

• Prerequisites of NP-nets• Ostensive definition of NP-nets: Simple model of P2P

protocol• Formal definition of NP-nets• Need for analysis methods• Compositionality of NP-net properties• Technical achievements• Conclusions and further directions

Page 68: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.58

Technical achievements: NPN2CPN

• Idea: we don’t have any tools at all, so why don’t translateNP-nets to models with tool support

• What tool? - CPNtools• Why? - Simulation, Performance analysis, Reachability

graph, CTL model checking et cetera.• Implementation of the translation: Hattu Pavel, Sysoev

German.

Page 69: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.58

Technical achievements: NPN2CPN

• Idea: we don’t have any tools at all, so why don’t translateNP-nets to models with tool support

• What tool?

- CPNtools• Why? - Simulation, Performance analysis, Reachability

graph, CTL model checking et cetera.• Implementation of the translation: Hattu Pavel, Sysoev

German.

Page 70: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.58

Technical achievements: NPN2CPN

• Idea: we don’t have any tools at all, so why don’t translateNP-nets to models with tool support

• What tool? - CPNtools

• Why? - Simulation, Performance analysis, Reachabilitygraph, CTL model checking et cetera.

• Implementation of the translation: Hattu Pavel, SysoevGerman.

Page 71: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.58

Technical achievements: NPN2CPN

• Idea: we don’t have any tools at all, so why don’t translateNP-nets to models with tool support

• What tool? - CPNtools• Why?

- Simulation, Performance analysis, Reachabilitygraph, CTL model checking et cetera.

• Implementation of the translation: Hattu Pavel, SysoevGerman.

Page 72: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.58

Technical achievements: NPN2CPN

• Idea: we don’t have any tools at all, so why don’t translateNP-nets to models with tool support

• What tool? - CPNtools• Why? - Simulation, Performance analysis, Reachability

graph, CTL model checking et cetera.• Implementation of the translation: Hattu Pavel, Sysoev

German.

Page 73: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.59

Technical achievements: NPN2CPN

p0

xrx

xr

x

t2[ms_le_el [0,0,1,1] x]

input(x);output(xr);actionlet val rs = ms_add(x,[1,1,~1,0]);in (rs)end;

t1

[ms_le_el [1,0,0,0] x]

input(x);output(xr);actionlet val rs = ms_add(x,[~1,1,1,0]);in (rs)end;

p0

[3,0,0,2]

LIST_INT

1 1`[3,0,0,2]

p1

p2

p3

p4

t1

τt2

τ

m:

α:

Page 74: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.60

Technical achievements: NPN2CPN

p0

p1

p2

T1

τx

y

x+ y

x

x ++ y

y

T1

p0

[3,0,0,2]

LIST_INT

p2

LIST_INT

p1

[1,0,0,1]

LIST_INT

1 1`[3,0,0,2] 1 1`[1,0,0,1]

p1

p2

p3

p4

t1

t2

m:

Page 75: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.61

Technical achievements: NPN2CPN

p0

p1

p2

t1

λ

x

x

y

y

LIST_INT

[2,0]

LIST_INT

LIST_INT

[3,0,0,2]

p2

T11

T12

[ms_le_el [0,0,1,1] x, ms_le_el [1,0] y]

input(x,y);output(xr,yr);actionlet val rs1 = ms_add(x,[1,1,~1,0]); val rs2 = ms_add(y,[~1,1]);in (rs1,rs2)end;

p1

p0

xxr

x

y

y

yr

yrxr

[ms_le_el [1,0,0,0] x, ms_le_el [1,0] y]

input(x,y);output(xr,yr);actionlet val rs1 = ms_add(x,[~1,1,1,0]); val rs2 = ms_add(y,[~1,1]);in (rs1,rs2)end;

1 1`[2,0]

1 1`[3,0,0,2]

p3

p4

p5

p6

λ

t2λ

t3

p7 p8

λ

t4

m:

Page 76: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.62

Technical achievements: NPN2CPN

Source NP-net:

p1

p2

p3t1

λ

t2

λ

t3

λ

p4 p5t4

λ

t5

λ

p6

p7

p8

p9

p10

p11 p12

p13

p14 p15

t6

t7 t8 t9

t10 λ

t11 λ

t12λ

p16

p17

p18

p19

p20

p21

p22

p23

t14 λ

x

y

z

x

y

z

t15 λy

y

t16 λ

x

y

z

x

y

z

t17 λ

z

z

E1(seed):

E2(peer):E3(pipe):

SN(protocol):

Page 77: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.63

Technical achievements: NPN2CPN

Resultant CP-net:

Page 78: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.64

Technical achievements: EMF model

• It would be better to have our own tool;

• We have to start from a data model;

Page 79: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.64

Technical achievements: EMF model

• It would be better to have our own tool;• We have to start from a data model;

Page 80: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.65

Technical achievements: EMF model

Page 81: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.66

Technical achievements

• It would be better to have our own tool;• We have to start from a data model;• Haskell backend (by Daniil Frumin);

1 Model checking of separate components;2 Compositional checking of NP-nets liveness (alpha-trail

nets, m-bisimulation algorithm).

Page 82: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.67

Technical achievements

• It would be better to have our own tool;• We have to start from a data model;• Haskell backend (by Daniil Frumin);• Graphical editor (by Ilya Zubarev);

Page 83: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.68

Technical achievements: Eclipse editor

Page 84: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.69

Technical achievements

• It would be better to have our own tool;• We have to start from a data model;• Haskell backend (by Daniil Frumin);• Graphical editor (by Ilya Zubarev);• Analysis of components (by Anton Fillipov);

• reachability graph, reachability tree, coverability tree,P-invariants, covering P-invariants, (extended)free-choiceness checking.

Page 85: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.70

Technical achievements: EMF model

Page 86: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.71

Technical achievements

• It would be better to have our own tool;• We have to start from a data model;• Haskell backend (by Daniil Frumin);• Graphical editor (by Ilya Zubarev);• Analysis of components (by Anton Fillipov);• Code generation:

• From NP-nets to Java apps over TCP/IP (by DmitryKuznecov)

• From NP-nets to EJB system (by Nikolenko Artem)

Page 87: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.72

Whats the Plan?

• Prerequisites of NP-nets• Ostensive definition of NP-nets: Simple model of P2P

protocol• Formal definition of NP-nets• Need for analysis methods• Compositionality of NP-net properties• Technical achievements• Ongoing research• Conclusions and further directions

Page 88: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.73

Ongoing research

1 Compositionality of P-invariants for NP-nets;2 Compositionality of T-invariants for NP-nets;3 Time NP-nets;4 Compositional bounding of unbounded NP-nets by timing;

Page 89: Methods of Analysis for Nested Petri Nets (NP-nets) · Sci. Advisor: I. A. Lomazova (ilomazova@hse.ru) National Research University Higher School of Economics. Methods of Analysis

Methods of Analysisfor

Nested Petri Nets(NP-nets)

Preface

Prerequisites ofNP-nets

Simple model of P2Pprotocol

Definition of NestedPetri Net (NP-net)

Need for analysismethods

Compositionality ofNP-net properties

Technicalachievements

Ongoing research

Conclusions

1.74

Conclusions and further directions

1 Nested Petri Nets with well-formed components can beanalysed for boundedness and liveness in polynomialtime;

2 Boundedness and liveness holds compositionality forNP-nets (under some constraints)

3 Compositionality of:• P- and T- invariants;• Fairness, impairness, justice.