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The Universality Problem is the dual of the emptiness problem: is L(A) = Σ∗?
It can be solved by minor variations of any one of the algorithms for Emptiness or (with a little less work) it can simply be reduced to Emptiness.
Theorem (Universality) The Universality Problem for Regular Languages is decidable.
Proof: L(A) = Σ*⇔ L(A) = ∅. As regular languages are effectively closed under complement we can simply build the DFA for the complement of L(A) and ask if it recognizes the empty language.
Intuitively, closure of SL 2 under intersection is reasonably easy to see, particularly if one considers the Myhill graphs of the automata. Any path through both graphs will be a
Kleene called this the Synthesis theorem because his (and your) proof gives an effective procedure for synthesizing an automaton that recognizes the language denoted by any given r
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Give the Myhill graph of your automaton. (You may use a single node to represent the entire set of symbols of the English alphabet, another to represent the entire set of decima
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Find the Regular Grammar for the following Regular Expression: a(a+b)*(ab*+ba*)b.
We will assume that the string has been augmented by marking the beginning and the end with the symbols ‘?' and ‘?' respectively and that these symbols do not occur in the input al
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