Question

Construct a regular expression that recognizes the following language of strings over the alphabet {0 1}:
The language consisting of the set of all bit strings that start with 00 or end with 101 (or both).

Syntax

The union is expressed as R|R, star as R*, plus as R+, concatenation as RR.
Epsilon is not supported but you can write R? for the regex (R|epsilon).

Answer 1

Regular expression to recognize language L= {The language consisting of the set of all bit strings that start with 00 or end with 101 (or both)} over the alphabet {0, 1}

= (00(0|1)*(101)*) | ((00)*(0|1)*(101))

Understanding the above regex:

The regex mainly consists of two parts, one on the left of | and one on the right of it.

The left part is (00(0|1)*(101)*)

The right part is ((00)*(0|1)*(101))

The left part is the regular expression to recognize all strings over {0, 1} which starts with 00 and may or may not end with a 101.

The right part is the regular expression to recognize all strings over {0, 1} which may or may not start with 00 but always ends with 101.

The union of the left and right parts gives us a regular expression to recognize the language L.