UNIT-I Finite State Machines - Impetus & Bank Unitwise.pdf · PDF file 2019. 3....

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Transcript of UNIT-I Finite State Machines - Impetus & Bank Unitwise.pdf · PDF file 2019. 3....

  • UNIT-I Finite State Machines

    Q.1) Construct a deterministic finite automata (DFA) that recognizes the language

    L= {x ϵ (0,l) | (x contains at least two consecutive 0’s) and (x does not contain two

    consecutive l’s)} (4 Marks Aug-2015 INSEM)

    Q.2) Convert the given NFA−ε to an NFA. (6 Marks Aug-2015 INSEM)

    Q.3) Minimize the following automata. (4 Marks Aug-2015 INSEM)

    Q.4) Convert Following Moore Machine into Mealy Machine. (6 Marks Aug-2015

    INSEM)

    Present State Next State

    Output a = 0 a = 1

    -> q0 q3 q1 1

    q1 q2 q3 0

    q2 q2 q1 0

    q3 q1 q0 1

    Q.5) Define and compare NFA and DFA. (4 Marks Aug-2014 INSEM)

  • Q.6) Design finite automation for the following (6 Marks Aug-2014 INSEM)

    i. FA which reads strings made up of {0, l} and accepts only those strings which end in either ‘00’ or ‘ll’.

    ii. FA which accepts only those strings with ‘a’ at every even position. ∑={a,b}.

    Q.7) Define and compare Moore and Mealy machines. (4 Marks Aug-2014

    INSEM)

    Q.8) Construct Mealy machine equivalent to the given Moore machine. (6 Marks

    Aug-2014 INSEM)

    0 1 O/P

    q0 q0 q1 N

    q1 q0 q2 N

    q2 q0 q3 N

    q3 q0 q3 Y

    Start state : q0 ; Final state : q3

    Q.9) Define the following terms. (6 Marks May-2013,2016 ENDSEM)

    1) Symbol 2) Language 3) Kleene closure

    Q.10) Design a Finite Automata FA which accepts odd number of 0’S an even

    number of 1’s. (6 Marks May-2013 ENDSEM)

    Q.11) Design NFA which accepts the string containing either “01” or “10” over

    Σ={0,1}. (6 Marks May-2013 ENDSEM)

    Q.12) Convert the following mealy machine into equivalent Moore machine. (6

    Marks May-2013 ENDSEM)

  • Q.12) Construct an equivalent DFA for given NFA

    M={{q, p, r, s, t},{0,1},𝛿,p,{t}}

    where 𝛿 is defined in the following table. (6 Marks May-2013 ENDSEM)

    𝛿 0 1

    {p}

    {t}

    {q,r}

    𝜙

    {p,s}

    {p,t}

    {t}

    𝜙

    𝜙

    𝜙

    {p,t}

    {t}

    {q,r}

    𝜙

    {p,s}

    𝜙

    {q,r}

    {q,r}

    Q.13) Construct Moore machine equivalent for the given Mealy machine. (6 Marks

    May-2015 ENDSEM)

    Q. 14 Design a DFA for accepting L over {0,l} such that every substring of length 4

    contains at least three l’s. . (4 Marks May-2015 ENDSEM)

    Q.15) Construct NFA accepting language represented by 0*l*2* and convert it into

    DFA. (6 Marks May-2015 ENDSEM)

    Q.16) Explain the Basic Finite Automata? What are the various application &

    limitation of it? (6 Marks May-2016 ENDSEM)

  • Q.16) Obtain a DFA equivalent to the NFA. (4 Marks May-2016 ENDSEM)

    Q.17) Construct FA that accepts even number of zeros & odd number of ones. (4

    Marks May-2017 ENDSEM)

    Q.18) Construct a Moore machine to find out the residue-modulo-3 for binary

    number. (6 Marks May-2017 ENDSEM)

    Q.19) Define regular sets. List out closure properties of regular sets. (4 Marks May-

    2017 ENDSEM)

    Q.20) Design a DFA that read strings made up of I = {0, 1} and accept only those

    strings which ends with 00 or 11. (8 Marks Nov-2014 ENDSEM)

    Q.21) State and explain properties of FSM. (2 Marks Nov-2014 ENDSEM)

    Q.22) Design a finite state machine for divisibility by 5 tester of a given decimal

    number. (8 Marks Nov-2014 ENDSEM)

    Q.23) Design a Mealy machine to accept binary strings having 101 or 110 as

    substring. (8 Marks Nov-2014 ENDSEM)

    Q.24) Convert following NFA into equivalent DFA,

    M = ({q0, q1,}, {0,1,}, δ, q0, {q1}) where

    δ (q0, 0) = {q0, q1,}

    δ (q0,1,) = {q1}

    δ (q1,1) = { q0, q1}

    (8 Marks Nov-2014 ENDSEM)

  • Q.25) Construct the minimum state automation equivalent to the transition diagram

    given as below:

    (6 Marks Nov-2014 ENDSEM)

    Q.26) Design an FA for the languages that contain strings with next-to-last symbol 0. (5 Marks Nov-2015 ENDSEM)

    Q.27) Write formal definition of NFA - 2. Also define ε – closure.

    (5 Marks Nov-2015 ENDSEM)

    Q.28) Draw an FA recognizing the regular language corresponding to give regular

    expression. (5 Marks Nov-2015 ENDSEM)

    1(01 + 10)* + 0 (11 + 10)*

    Q.29) Design FA/FSM accept only those strings which ending with “abb” over input =

    {a, b}. (8 Marks Nov-2016 ENDSEM)

    Q.30) Design a finite automata which perform addition of two Binary number. (8 Marks

    Nov-2016 ENDSEM)

    Q.31) Define Finite State Machine. Explain its properties and limitations. (4 Marks

    Nov-2016 ENDSEM)

    Q.32) Design a Mealy machine to check divisibility of decimal number by 4. (8 Marks

    Nov-2016 ENDSEM)

    Q.33) Construct NFA and its equivalent DFA for accepting a language defined over input

    = {0, l} such that each string has two consecutive zeros followed by l. (8 Marks Nov-

    2016 ENDSEM)

    Q.34) Construct a deterministic finite automata (DFA) for accepting L over (0, l) such that

    every substring of length 4 contains at least three l’s. (6 Marks Nov-2016 ENDSEM)

  • Q.35) Construct Moore machine for given Mealy machine. (6 Marks Nov-2016 ENDSEM)

    Q.36) Define the following with suitable examples. (4 Marks Nov-2017 ENDSEM)

    i) FA

    ii) Regular Expression

    Q.37) Convert Mealy machine to Moore machine. (6 Marks Nov-2017 ENDSEM)

    Q.38) Design Moore machine for divisibility by 3 tester for binary number. (6 Marks Nov-

    2017 ENDSEM)

    Q.39) Design Finite Automata to accept strings ending with 00 or ll. (4 Marks Nov-2017

    ENDSEM)

  • UNIT-II Regular Expressions

    Q.1) Construct DFA for the R.E l0 + (0 + ll) ( 6 Marks Nov-2016)

    Q.2) State the pumping lemma theorem for regular sets. Show that the language L =

    {0n | n is prime} is not regular. (4 Marks Nov-2016)

    Q.3) Using Pumping lemma, Prove that L = {Oi 2

    / i is an integer, i > l} is not-

    regular. (6 Marks NOV-2017)

    Q.4) Discuss Applications of FA & regular expressions. (4 Marks NOV-2017)

    Q.5) Define the following with suitable examples (4 Marks NOV-2017)

    i. FA ii. Regular Expression

    Q.6) Find the regular expression for the following: (4 Marks NOV-2017)

    i)

    ii)

    Q.7) Prove that the following language is non-regular, using pumping lemma.

    L = {anbn |n>0} (6 Marks NOV-2017)

    Q.7) Show that (0 +l)* = (0* l*)* (4 Marks Nov-2016)

    Q.8) Give RE for following language over = {0, l} (6 Marks Nov-2016)

    i. The language of all strings containing exactly two 0’s. ii. The language of all strings containing at least two 0’s.

    iii. The language of all strings not containing the substring 00

  • Q.8) Draw an FA recognizing the regular language corresponding to give regular

    expression. (5 Marks NOV-2015)

    1(01 + 10)* + 0 (11 + 10)*

    Q.9) Write a short note on the applications of Regular Expressions. (5 Marks NOV-

    2015)

    Q.10) Using Pumping lemma for the regular sets Prove the language L = {ai 2

    | i is

    an integer, i ≥ l} is not- regular. (6 Marks NOV-2015)

    Q.11) Construct Regular Expression for the following transition diagram using

    Arden’s theorem. (4 Marks NOV-2015)

    Q.12) What is Regular Expression ‘r’. Give RE for the following language over {0,

    1}. (6 Marks NOV-2014)

    i. Language of all strings that begin and end with 101. ii. If L(r) = {00, 010, 0110, 01110, .....}.

    Q.13) Show that (a* b*)*=(a +b)* (4 Marks Nov-2014)

    Q.14) Construct DFA for regular expression (a + b)* abb. (8 Marks Nov-2014)

    Q.15) Construct NFA for following regular expressions. (8 Marks Nov-2014)

    i. a * b (a + b)* ii. (aa + bb)* bb (a + b)*

    Q.16) Explain properties of regular expression. (6 Marks Nov-2014)

    Q.17) Write formal definition of regular expression with suitable example. State

    Arden’s theorem and its use. (4 Marks May-2017)

  • Q.18) Define regular sets. List out closure properties of regular sets. (4 Marks May

    -2017)

    Q.19) Describe in the simple English the language defined by the following RE.

    (6 Marks May-2016)

    i. (a+b)* a (a+b)* ii. (01*0)* 1

    iii. a(a+b)*bb

    Q.20) Construct a FA for given regular expression (10)* 101(01)*. (4 Marks May-

    2016)

    Q.21) Let ∑ = {a,b}. Write RE to define language consisting of strings such that

    i. Strings without substring bb ii. Strings that have exactly one double letter in them.

    (4 Marks May-2015)