Zino H. Hu
Abstract
An automaton is isomorphic to the direct product of a permutation strongly connected automaton and a synchronizing strongly connected automaton if and only if it is strongly connected; the minimal ideal of its input semigroup has a single R-class and the ranges of its minimal rank input functions form a partition on its set of states.
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An automaton is isomorphic to the direct product of a permutation strongly connected automaton and a synchronizing strongly connected automaton if and only if it is strongly connected; the minimal ideal of its input semigroup has a single R-class and the ranges of its minimal rank input functions form a partition on its set of states.
Key concepts: Mathematics, Büchi automaton, Deterministic automaton, Direct product, Automaton, Two-way deterministic finite automaton, Semigroup, Continuous automaton