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In Exercise 9 you showed that the recognition problem and universal recognition problem for SL2 are decidable. We can use the structure of Myhill graphs to show that other problems
Given any NFA A, we will construct a regular expression denoting L(A) by means of an expression graph, a generalization of NFA transition graphs in which the edges are labeled with
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Claim Under the assumptions above, if there is an algorithm for checking a problem then there is an algorithm for solving the problem. Before going on, you should think a bit about
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
design an automata for strings having exactly four 1''s
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
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State & prove pumping lemma for regular set. Show that for the language L={ap |p is a prime} is not regular
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
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