At this point we would like to find out answers to some important questions related to regular languages. The questions we consider here all have answers which may be either “yes” or “no”. These are known as decision problems since we used to decide whether the answer is “yes” or “no”. [The reason for considering decision problems is that a regular language is recognized by a FA, which, in response to an input string, either ‘accepts' or ‘rejects' the input string and can be considered as producing “yes” or no “answers”, respectively.]

Consider the following typical and important question:

w and a regular language L , is an element of L ?

The answer is either yes or no.

While w is represent explicitly, we wonder how L given to us. Obviously, L cannot be given as an enumeration of strings (L may be infinite). L will be represented either by a DFA , NFA or regular expression.

The question presented above is called the “membership problem” for the corresponding regular language L.

If L is represented by a DFA , the problem has an easy solution-