GATE CS 2016 Set 1 — Question 28
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Theory of Computation → Finite Automata & Regular Languages → Regular Expressions
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Question
Which one of the following regular expressions represents the language: the set of all binary strings having two consecutive 0s and two consecutive 1s?
Correct answer
(B) (0+1)^ (00(0+1)^ 11+11(0+1)^ 00)(0+1)^
Solution
The problem asks for strings containing both "00" and "11" as substrings.Since both substrings must appear, there are two mutually exclusive cases regarding their relative order:
1."00" appears before "11". The pattern is: (anything) followed by "00", followed by (anything), followed by "11", followed by (anything).
Regex: 2."11" appears before "00". The pattern is: (anything) followed by "11", followed by (anything), followed by "00", followed by (anything).
Regex: The union of these two cases covers all valid strings.Option (B) combines these:This matches the logic exactly.Why other options are incorrect:- (A) requires "00" and "11" to be immediately adjacent (e.g., "0011" or "1100"). It misses strings like "001011".
- (C) represents strings containing "00" OR "11". The question requires AND.
- (D) forces the string to start with one pattern and end with the other. It misses strings like "100110".
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