Question

Which of the following pairs of regular expressions are equivalent?

(a) 1(01)* and (10)*1

(b) x (xx)* and (xx)*x

(c) x^+ and x^+ x^(*+)

(d) All of the mentioned

The question was asked in semester exam.

Enquiry is from Finite Automata and Regular Expressions in division Compiler Introduction of Compiler

Answer 1

Correct option is (d) All of the mentioned

For explanation: Rule (pq)*p=p (qp)*

Therefore–(xx*) (x*x**)

(xx*)(x*x*)  [Using x**=x]

(xx*)(x*)     [Using x*x*=x*]

(xx*)           [Using x*xx*=x*)

x+