Bogdanović, Stojan

Petković, Tatjana

Ćirić, Miroslav

English

The purpose of this paper is to describe structural properties of automata whose transition semigroups have a zero, left zero, right zero or bi-zero, or are nilpotent extensions of rectangular bands, left zero bands or right zero bands, or are nilpotent. To describe the structure of these automata we use various well-known decomposition methods of automata theory - direct sum decompositions, subdirect and parallel decompositions, and extensions of automata. Automata that appear as the components in these decompositions belong to some well-known classes of automata, such as directable, definite, reverse definite, generalized definite and nilpotent automata. But, we also introduce some new classes of automata: generalized directable, trapped, onetrapped, locally directable, locally one-trapped, locally nilpotent and locally definite automata. We explain relationships between the classes of all these automata

Petković Tatjana

Ćirić Miroslav

Bogdanović Stojan

University of Szeged

Decompositions of automata and transition semigroups

http://acta.bibl.u-szeged.hu/12598/1/cybernetica_013_numb_004_385-403.pdf

Decompositions of automata and transition semigroups

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University of Szeged