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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.
Construct a Mealy machine that can output EVEN or ODD According to the total no. of 1''s encountered is even or odd.
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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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