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Group automata and near-rings. (English) Zbl 0574.68051
Proc. Klagenfurt Conf. 1982, Contrib. Gen. Algebra 2, 153-162 (1983).
[For the entire collection see Zbl 0512.00011.]
It is well known that semigroups are very useful in the study of automata. These semigroups consist of mappings from the state set Q of the automaton into itself. If, as is often the case, Q bears the structure of a group, we are studying mappings of a group into itself and the natural algebraic tool to use is a near-ring. In this paper our aim is to show how natural near-rings and group automata can be linked by generalizing ideas of M. Holcombe [Proc. Edinb. Math. Soc., II. Ser. 26, 15-24 (1983; Zbl 0491.16034)].

MSC:
68Q70 Algebraic theory of languages and automata
20M35 Semigroups in automata theory, linguistics, etc.
16Y30 Near-rings