GATE CS 2021 Set 1 — Question 48
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Theory of Computation → Finite Automata & Regular Languages → DFA
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Question
Consider the following language.Which one of the following deterministic finite automata accepts ?
Correct answer
(D) [figure]
Solution
The language consists of all strings over that end with the substring . To construct a DFA for this language, the states typically represent the longest suffix of the input string read so far that matches a prefix of .Let the states be:
- : No part of the suffix has been matched (or the last symbol was but not preceded by ).
- : The string ends in .
- : The string ends in .
- : The string ends in (accepting state).
- From : input , input .
- From : input , input .
- From : input (since ends in ), input .
- From : input (since ends in ), input (since ends in ).
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