GATE CS 2014 Set 3 — Question 25
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Theory of Computation → Finite Automata & Regular Languages → Regular Expressions
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Question
The length of the shortest string NOT in the language (over ) of the following regular expression is ______________.
Correct answer
3 to 3
Solution
Let the language be . We check strings of increasing length over :
- Length 0: is in (take all exponents as ).
- Length 1: (), () are in .
- Length 2:
- ()
- ()
- ()
- ()
- Length 3:
- ()
- ()
- ()
- ()
- ()
- : To form , the first must come from or . If from , we need from , which is impossible. If from , it must be , leaving to be matched by , which is impossible. Thus, .
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