GATE CS 2015 Set 2 — Question 45
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Theory of Computation → Finite Automata & Regular Languages → DFA Minimization
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Question
The number of states in the minimal deterministic finite automaton corresponding to the regular expression is ________.
Correct answer
3 to 3
Solution
The regular expression represents the set of all binary strings ending with the substring .To construct the minimal DFA:
1.State (Start): Represents the state where we have not seen the pattern or the last symbol was (and not part of a ).
- On input , stay in .
- On input , go to .
- On input , we complete the pattern , so go to .
- On input , we still have a suffix , so stay in .
- On input , the suffix becomes (ends in ), go to .
- On input , the suffix becomes (ends in ), go to .
- : start state
- : intermediate state
- : accepting state
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