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2013•Journal of Mathematical and Computational ScienceRequires access

ISOMORPHISMS ON STRONGLY CONNECTED GROUP AUTOMATON

S. Jeya Bharathi, A. Jeyanthi

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Abstract

Direct product of a permutation strongly connected automaton and a synchronizing strongly connected Aleshin Type automaton is also a strongly connected automaton. An automaton is called quasi-ideal  automaton if and only if all the following conditions are satisfied; (i) It is strongly connected (ii) the minimal ideal of its transition semi group is a right group (iii) the ranges of the idempotent elements of the minimal ideal of its transition group form a merging of a partition on its set of states. An automaton is isomorphic to the direct product of a permutation strongly connected automaton and synchronizing strongly connected Aleshin type automaton if and only if it is a quasi ideal automaton.

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What this paper is about

Direct product of a permutation strongly connected automaton and a synchronizing strongly connected Aleshin Type automaton is also a strongly connected automaton. An automaton is called quasi-ideal  automaton if and only if all the following conditions are satisfied; (i) It is strongly connected (ii) the minimal ideal of its transition semi group is a right group (iii) the ranges of the idempotent elements of the minimal ideal of its transition group form a merging of a partition on its set of states. An automaton is isomorphic to the direct product of a permutation strongly connected automaton and synchronizing strongly connected Aleshin type automaton if and only if it is a quasi ideal automaton.

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Available abstract

Direct product of a permutation strongly connected automaton and a synchronizing strongly connected Aleshin Type automaton is also a strongly connected automaton. An automaton is called quasi-ideal  automaton if and only if all the following conditions are satisfied; (i) It is strongly connected (ii) the minimal ideal of its transition semi group is a right group (iii) the ranges of the idempotent elements of the minimal ideal of its transition group form a merging of a partition on its set of states. An automaton is isomorphic to the direct product of a permutation strongly connected automaton and synchronizing strongly connected Aleshin type automaton if and only if it is a quasi ideal automaton.

Key concepts: Mathematics, Büchi automaton, Block cellular automaton, Continuous automaton, Deterministic automaton, Timed automaton, Two-way deterministic finite automaton, Reversible cellular automaton

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