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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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Computation of a DFA or NFA without ε-transitions An ID (q 1 ,w 1 ) computes (qn,wn) in A = (Q,Σ, T, q 0 , F) (in zero or more steps) if there is a sequence of IDs (q 1
So we have that every language that can be constructed from SL languages using Boolean operations and concatenation (that is, every language in LTO) is recognizable but there are r
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Trees and Graphs Overview: The problems for this assignment should be written up in a Mircosoft Word document. A scanned hand written file for the diagrams is also fine. Be
Another way of interpreting a strictly local automaton is as a generator: a mechanism for building strings which is restricted to building all and only the automaton as an inexh
Paths leading to regions B, C and E are paths which have not yet seen aa. Those leading to region B and E end in a, with those leading to E having seen ba and those leading to B no
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
The fact that the Recognition Problem is decidable gives us another algorithm for deciding Emptiness. The pumping lemma tells us that if every string x ∈ L(A) which has length grea
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