On Direct Product and Quotient of Strongly Connected Automata

Details On Direct Product and Quotient of Strongly Connected Automata On Direct Product and Quotient of Strongly Connected Automata

2011-04-17

arxiv.org/abs/1104.3314v8

Computer Science

Formal Languages and Automata Theory

6 pages

Scientific paper

An automaton is isomorphic to the direct product of a permutation strongly connected automaton and a synchronizing strongly connected automaton if and only if all of these three conditions are met: (i) it is strongly connected; (ii) the minimal ideal of its input semigroup has a single R-class and (iii) the ranges of the idempotent elements of the minimal ideal of its input semigroup form a partition on its set of states.

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