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Sketch an algorithm for the universal recognition problem for SL2. This takes an automaton and a string and returns TRUE if the string is accepted by the automaton, FALSE otherwise. Assume the automaton is given just as a sequence of pairs of symbols and that the automaton and string are both over the same language. Give an argument justifying the correctness of your algorithm.
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Theorem The class of ?nite languages is a proper subclass of SL. Note that the class of ?nite languages is closed under union and concatenation but SL is not closed under either. N
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Another striking aspect of LTk transition graphs is that they are generally extremely ine?cient. All we really care about is whether a path through the graph leads to an accepting
Theorem (Myhill-Nerode) A language L ⊆ Σ is recognizable iff ≡L partitions Σ* into ?nitely many Nerode equivalence classes. Proof: For the "only if" direction (that every recogn
The universe of strings is a very useful medium for the representation of information as long as there exists a function that provides the interpretation for the information carrie
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Both L 1 and L 2 are SL 2 . (You should verify this by thinking about what the automata look like.) We claim that L 1 ∪ L 2 ∈ SL 2 . To see this, suppose, by way of con
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