Automata Theory Construct a regular expression for the set of bit strings in which every odd...
Automata Theory
Construct a regular expression for the set of bit strings in which every odd bit is 1.
For example, these are in the language:
10 (OK: 1 in position 1)
111 (OK: 1 in positions 1 and 3)
10101 (OK: 1 in positions 1, 3, and 5)
101111 (OK: 1 in positions 1, 3, and 5)
ϵ (OK: There are no odd positions)
And these are not in the language:
0111 (BAD: position 1 is not a 1)
110 (BAD: position 3 is not a 1)
011001 (BAD: position 1 is not a 1 (nor is position 5))
Homework Answers
Regular Expression: (1(0+1))*
Explanation
Odd bit is 1
Even bit can be any of 0 and 1: (0+1)
Any number of occurrences of above can come. So, * is used
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following FA: (see picture for diagram)
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