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Let Sigma be a finite alphabet and let L 0 , L 1 Sigma be languages such that L 0 cap L
Let Sigma be a finite alphabet and let L LSigma
be languages such that Lcap L Think of L
and L as the sets of bad and good strings respectively. We wish to design an automaton which
is guaranteed to reject every string in L and accept every string in L Our automaton is allowed to
behave arbitrarily on strings that are neither in L nor in L In other words, our automaton is required
to recognize some language L Sigma
such that L cap L and L L
For concreteness, let us say that we are looking for a DFA over the alphabet Sigma Also, let
Lx in
the number of s and s in x are unequal and L
n
n n in N cup
Observe that Lcap L Does there exist such a DFA which accepts every string in L and rejects
every string in L Prove your answer.
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