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- W97842182 abstract "AbstractThe purpose of this paper is to describe structural properties of automatawhose transition semigroups have a zero, left zero, right zero or bi-zero, orare nilpotent extensions of rectangular bands, left zero bands or right zerobands, or are nilpotent. To describe the structure of these automata we usevarious well-known decomposition methods of automata theory – direct sumdecompositions, subdirect and parallel decompositions, and extensions of au-tomata. Automata that appear as the components in these decompositionsbelong to some well-known classes of automata, such as directable, definite,reverse definite, generalized definite and nilpotent automata. But, we alsointroduce some new classes of automata: generalized directable, trapped, one-trapped, locally directable, locally one-trapped, locally nilpotent and locallydefinite automata. We explain relationships between the classes of all theseautomata.Keywords: automaton, transition semigroup, direct sum decomposition,directable automata, trapped automata, generalized directable automata, lo-cally directable automata, generalized varieties," @default.
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- W97842182 date "1999-01-01" @default.
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- W97842182 title "Decompositions of automata and transition semigroups" @default.
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