Right group-type automata

  I. Babcsányi A. Nagy

Abstract:

  In this paper we deal with state-independent automata whose characteristic semigroups are right groups (left cancellative and right simple). These automata are called right group-type automata. We prove that an A-finite automaton is state-independent if and only if it is right group-type. We define the notion of the right zero decomposition of quasi-automata and show that the state-independent automaton is right group-type if and only if the quasi-automaton corresponding to is a right zero decomposition of pairwise isomorphic group-type quasi-automata. We also prove that the state-independent automaton is right group-type if and only if the quasi-automaton corresponding to is a direct sum of pairwise isomorphic strongly connected right group-type quasi-automata. We prove that if is an A-finite state-independent automaton, then is a divisor of . Finally, we show that the quasi-automaton corresponding to an A-finite state-independent automaton is a right zero decomposition of pairwise isomorphic quasi-perfect quasi-automata if and only if .

 Gyenizse Pal 1996. Augusztus 28. Szerda 14:09:16 MET DST