Abstract

Hypergraphic automata are automata, state sets and output symbol sets of which are hypergraphs, being invariant under actions of transition and output functions. Universally attracting objects of a category of hypergraphic automata are universal hypergraphic automata. The input symbol semigroup of such automaton is an algebra of mappings which is considered as a derivative algebraic system for such automaton. Semigroup properties of the derivative algebraic system are interconnected with properties of the automaton. Thus, we can obtain a lot of information about a universal hypergraphic automaton studying its input symbol semigroups. In this paper, we found an abstract characterization of universal hypergraphic automata and an abstract characterization of input symbol semigroups of such automata. The results of the paper present effective tools for further analysis of the interrelation of algebraic and elementary properties of universal hypergraphic automata and their input symbol semigroups.

中文翻译：

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通用超图自动机输入符号半群的抽象表征

摘要

超图自动机是自动机，其状态集和输出符号集是超图，在转移和输出功能的作用下是不变的。普遍的超图自动机吸引了一种超图自动机。这种自动机的输入符号半群是映射的代数，其被认为是这种自动机的导数代数系统。导数代数系统的半群性质与自动机的性质相互关联。因此，我们可以获得大量有关研究其输入符号半群的通用超图自动机的信息。在本文中，我们发现了通用超图自动机的抽象特征以及这种自动机的输入符号半群的抽象特征。