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We developed the idea of FSA by generalizing LTk transition graphs. Not surprisingly, then, every LTk transition graph is also the transition graph of a FSA (in fact a DFA)-the one in which the state set Q is just the set of nodes of the LTk transition graph. We get, as an immediate consequence, that every LT language (and, hence, every SL language and every ?nite language) is recognizable. In generalizing to arbitrary state sets, though, we have actually increased the power of our automata.
Strictly 2-local automata are based on lookup tables that are sets of 2-factors, the pairs of adjacent symbols which are permitted to occur in a word. To generalize, we extend the
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Suppose A = (Σ, T) is an SL 2 automaton. Sketch an algorithm for recognizing L(A) by, in essence, implementing the automaton. Your algorithm should work with the particular automa
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We'll close our consideration of regular languages by looking at whether (certain) problems about regular languages are algorithmically decidable.
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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
Suppose G = (N, Σ, P, S) is a reduced grammar (we can certainly reduce G if we haven't already). Our algorithm is as follows: 1. Define maxrhs(G) to be the maximum length of the
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