Question

This a question in a compiler class, principles techniques and tools

Are the following identities on regular expressions correct. explain why?

1.) abb*c = ab*c

2.) ( a | b | c)* = (( a | b | c) e)*

3.) ( aa | ab | ac) = a ( a | b | c | e)

Answer 1

1.) abb*c = ab*c

Not correct

-Counter example-
ac is accepted by ab*c
ac is not accepted by abb*c

2.) ( a | b | c)* = (( a | b | c) e)*

Not correct

-Counter example-
a is accepted by ( a | b | c)*
a is not accepted by (( a | b | c) e)*

3.) ( aa | ab | ac) = a ( a | b | c | e)

Not correct

-Counter example-
ae is accepted by a ( a | b | c | e)
ae is not accepted by ( aa | ab | ac)

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