GATE CS 2017 Set 2 — Question 25
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Theory of Computation → Finite Automata & Regular Languages → DFA
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Question
The minimum possible number of states of a deterministic finite automaton that accepts the regular language is ________.
Correct answer
8 to 8
Solution
The language consists of strings over where the 3rd character is 'a' and the total length of the string is at least 6 ().The states of the minimal DFA represent the progress towards meeting these conditions:
1.: Start state (length 0)
2.: After 1 character (length 1)
3.: After 2 characters (length 2)
4.: After 3 characters, where the 3rd character is 'a' (length 3)
5.: After 4 characters, where the 3rd character was 'a' (length 4)
6.: After 5 characters, where the 3rd character was 'a' (length 5)
7.: After 6 or more characters, where the 3rd character was 'a' (length ) — Final State
8.: Trap state for strings where the 3rd character is 'b'.
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