A regular expression can be defined recursively as (a) Base Case: basic elements

Question

A regular expression can be defined recursively as (a) Base Case: basic elements lambda and a sigma(i.e. symbols in the alphabet), (b) Recursive Step: the concatenation, union, or Kleene-star of regular expressions, (c) Closure: starting with basic elements, the application of the recursive step a finite number of times is also a regular expression. Give a regular expression for the set of strings over {a, b, c} in which the total number of b's and c's is three. Give a regular expression for the set of strings over {a, b} with an even number of as or an odd number of b's.

Explanation / Answer

7.

We have total 3 b's and/or c's and number of a can any.

a*(b + c)a*(b+ c)a*(b + c)a*

8. Either a is even or b is odd not both.

(aa+ab+ba+bb)

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