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The Learnability of Simple Deterministic Finite-Memory Automata

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概要 The present paper establishes the learnability of simple deterministic finitememory automata via membership and equivalence queries. Simple deterministic finite-memory automata are a subclass of deter...ministic finite-memory automata introduced by Kaminski and Francez [9] as a model generalizing finite-state automata to infinite alphabets. For arriving at a meaningful learning model we first prove the equivalence problem for simple deterministic finite-memory automata to be decidable by reducing it to the equivalence problem for finite-state automata. In particular, we present a decision algorithm taking as input any two simple deterministic finite-memory automata A and B which computes a number k from A and B as well as two finite state automata $ M_A , M_B $ over a finite alphabet $ Sigma $ of cardinality k such that A and B are equivalent iff $ M_A $ and $ M_B $ are equivalent over $ Sigma $. Next, we provide the announced learning algorithm and prove its running time to be polynomially bounded in the length of a longest counter example returned, in k, the number described above, and in n the number of states of a minimum deterministic finite state automata being consistent with the target language over a finite alphabet of cardinality k.続きを見る

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登録日 2009.04.22
更新日 2017.01.20