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In this paper we study the prefix codes and application of prefix codes for problem of machine learning for deterministic finite state automaton. We give an example for the problem of constructing an inverse morphism, also parameterized by the number of transitions of automata. We investigate the factorization of prefix codes can give more simple structure of DFA for understanding his behaviors. To verify the correctness of the proposed approach, we implemented a system computer algebra GAP that accurately performs the logical flow of algorithm cycle by cycle.
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