Question

Let A and B be regular languages. Is the set of strings of odd length from A beginning with 0 concatenated with the set of strings of even length from B ending with 0 a regular language (yes or no). Explain your answer sufficiently to convince me that you are correct

Answer 1

If A and B be regular languages, then the set of strings of odd length from A beginning with 0 concatenated with the set of strings of even length from B ending with 0 . Then, Yes the new regular expression is a regular language.

a*(ba*ba*)* for an even number of b

b*ab*(ab*ab*)* for an odd number of a

Explanation in Detail:

There is a systematic way to merge these two because every regular expression can be represented by a state machine and vice versa, and there is definitely a way to merge state machines so that the resulting state machine accepts if either of the two state machines accepts, but I can't recall how this is done directly on regular expressions.

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