GATE CS 2014 Set 1 — Question 46
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Theory of Computation → Finite Automata & Regular Languages → DFA to RE
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Question
Which of the regular expressions given below represent the following DFA?
I)
II)
III)
I)
II)
III)
Correct answer
(B) I and III only
Solution
The DFA has a start state and a final state . Transitions: , , , . This DFA accepts all strings that end in a 1.
- III) : Clearly represents all strings ending in 1. Correct.
- I) : reaches . The term represents loops from back to (either reading 1, or reading 0 then some 0s then 1). This correctly describes the language. Correct.
- II) : The first part requires all 0s to precede 1s. The second part requires the string to start with 1. This expression fails to generate strings like (starts with 0, has 0 after 1). Incorrect.
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