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Algebraic Structure Theory of Automata (Algebraic Systems and Theoretical Computer Science)

Masami Itō

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Abstract

The present paper $1S$ a survey artlcle on algebralc structures of automata In the first part, we conslder $representat_{1}ons$ of strongly connected automata and $m$ the second part, first we define the layers of an automaton Then we deal wlth the poset of subautomata of an automaton and we conslder the class of slngle bottom automata, and we $P^{roV1}de$ the composltlon of a slngle loop automaton and a strongly connected automaton together $wlth_{1}tsautomorph_{1}sm$ group keywords: automaton, strongly connected automaton, automorphlsm group of an automaton, layer of an automaton, group-matrlx type automaton, poset, subautomaton, semllattlce, slngle bottom automaton, decomposltlon of an automaton, composltlon of automata

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The present paper $1S$ a survey artlcle on algebralc structures of automata In the first part, we conslder $representat_{1}ons$ of strongly connected automata and $m$ the second part, first we define the layers of an automaton Then we deal wlth the poset of subautomata of an automaton and we conslder the class of slngle bottom automata, and we $P^{roV1}de$ the composltlon of a slngle loop automaton and a strongly connected automaton together $wlth_{1}tsautomorph_{1}sm$ group keywords: automaton, strongly connected automaton, automorphlsm group of an automaton, layer of an automaton, group-matrlx type automaton, poset, subautomaton, semllattlce, slngle bottom automaton, decomposltlon of an automaton, composltlon of automata

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The present paper $1S$ a survey artlcle on algebralc structures of automata In the first part, we conslder $representat_{1}ons$ of strongly connected automata and $m$ the second part, first we define the layers of an automaton Then we deal wlth the poset of subautomata of an automaton and we conslder the class of slngle bottom automata, and we $P^{roV1}de$ the composltlon of a slngle loop automaton and a strongly connected automaton together $wlth_{1}tsautomorph_{1}sm$ group keywords: automaton, strongly connected automaton, automorphlsm group of an automaton, layer of an automaton, group-matrlx type automaton, poset, subautomaton, semllattlce, slngle bottom automaton, decomposltlon of an automaton, composltlon of automata

Key concepts: Real algebraic geometry, Algebraic number, Algebraic theory, Automaton, Automata theory, Algebra over a field, Function field of an algebraic variety, Dimension of an algebraic variety

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