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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.
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Theorem The class of recognizable languages is closed under Boolean operations. The construction of the proof of Lemma 3 gives us a DFA that keeps track of whether or not a give
For example, the question of whether a given regular language is positive (does not include the empty string) is algorithmically decidable. "Positiveness Problem". Note that
A problem is said to be unsolvable if no algorithm can solve it. The problem is said to be undecidable if it is a decision problem and no algorithm can decide it. It should be note
phases of operational reaserch
The computation of an SL 2 automaton A = ( Σ, T) on a string w is the maximal sequence of IDs in which each sequential pair of IDs is related by |- A and which starts with the in
conversion from nfa to dfa 0 | 1 ___________________ p |{q,s}|{q} *q|{r} |{q,r} r |(s) |{p} *s|null |{p}
Exercise: Give a construction that converts a strictly 2-local automaton for a language L into one that recognizes the language L r . Justify the correctness of your construction.
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