Deterministic Finite Automata (DFA)
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Transcript of Deterministic Finite Automata (DFA)
Automata Theory and LogicDeterministic Finite Automata (DFA)
A TUTORIAL
BY
ANIMESH CHATURVEDI
AT
INDIAN INSTITUTE OF TECHNOLOGY INDORE ( I IT - I )
Deterministic Finite Automata (DFA)
Representation of DFAM1 = (Q, Σ, δ, q1, F ) whereQ = {q1, q2, q3}, Σ = {0, 1},
the transition function δ is
Final state F = {q2}.
q1 is the start state, and F = {q2}.
0 1
q1 q1 q2
q2 q3 q2
q3 q2 q2
Example: Testing Membership
4
Start
1
0
A CB1
0 0,1
0 1 0 1 1
Nextsymbol
Currentstate
Example: Testing Membership
5
Start
1
0
A CB1
0 0,1
0 1 0 1 1
Nextsymbol
Currentstate
Example: Testing Membership
6
Start
1
0
A CB1
0 0,1
0 1 0 1 1
Nextsymbol
Currentstate
Example: Testing Membership
7
Start
1
0
A CB1
0 0,1
0 1 0 1 1
Nextsymbol
Currentstate
Example: Testing Membership
8
Start
1
0
A CB1
0 0,1
0 1 0 1 1
Nextsymbol
Currentstate
Example: Testing Membership
9
0 1 0 1 1
Nextsymbol
Currentstate
Start
1
0
A CB1
0 0,1
SLIDE BY STEVEN RUDICH: WWW.CS.CMU.EDU/~RUDICH RUDICH0123456789
00,1
00
1
1
1
0111 111
11
1
The machine accepts a string if the
process ends in a double circle
Build a DFAaccepts the set of all strings over {0,1} that end with 00
Computer Science GATE 2009
Build a DFAaccepts the set of all strings over {0,1} that end with 00
Computer Science GATE 2009
Minimal DFADraw a minimal DFA which accepts the same language as a DFA with alphabet ∑ = {a,b} is given below
Computer Science GATE 2011
Minimal DFADraw a minimal DFA which accepts the same language as a DFA with alphabet ∑ = {a,b} is given below
Computer Science GATE 2011
Number of statesDefinition of a language L with alphabet {a} is given as followingL = {ank | k > 0, and n is a positive integer constant}What is the minimum number of states needed in a DFA to recognize L?
Computer Science GATE 2011
Number of statesDefinition of a language L with alphabet {a} is given as followingL = {ank | k > 0, and n is a positive integer constant}What is the minimum number of states needed in a DFA to recognize L?
n+1 states are needed in a DFA to recognize L
Let n = 3 and k=1
3+1 = 4 states
Computer Science GATE 2011
Find missing arksConsider the set of strings on {0,1} in which, every substring of 3 symbols has at most twozeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings oflength less than 3 are also in the language. Draw the missing arks to complete a partially completed DFA given belowlanguage is shown below.
Computer Science GATE 2012
Find missing arksConsider the set of strings on {0,1} in which, every substring of 3 symbols has at most twozeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings oflength less than 3 are also in the language. Draw the missing arks to complete a partially completed DFA given below
Missing arksComputer Science GATE 2012
Find missing arksConsider the set of strings on {0,1} in which, every substring of 3 symbols has at most twozeros. For example, 001110 and 011001 are in the language, but 100010 is not. All strings oflength less than 3 are also in the language. Draw the missing arks to complete a partially completed DFA given below
Missing arksComputer Science GATE 2012
Up NextA DFA represent a Regular Expression language
Deterministic finite automata (DFA) and Non-deterministic finite automata (NFA) have sameexpressive power.
Deterministic and non-deterministic finite automata accept exactly the same set of languages.
DFA or NDFA has less expressive power than Deterministic push down automata (DPDA)