## Finite Automata; Behavior and Synthesis |

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absolute black boxes accessibility algorithm alphabet applied arbitrary assume automata automaton graph behavior black boxes bound Chapter clear concepts connected consider consisting constant construct contains corresponding defined definition denote described determine diagram distinguishable edges effectively empty ends equivalent estimate example exists Figure final finite automaton finite-state fixed formula frequency function given graph G identifies implies infinite initial input words issuing iterative labeled language least Lemma letter logn macrostate means metalanguage multiple natural number obtained Obviously occurrences operator output pair pairwise paths positive possible predicate probability problem proof prove realizes reduced regular expression relation representable representing residually respectively result sequence signaling function simple Stage step stochastic procedure symbols synthesis Theorem theory tree variables vertex vertices w-language w-word weight words of length