Self-regulating finite automata

Abstract

This paper introduces and discusses self-regulating finite automata. In essence, these automata regulate the use of their rules by a sequence of rules applied during previous moves. A special attention is paid to turns defined as moves during which a self-regulating finite automaton starts a new self-regulating sequence of moves. Based on the number of turns, the present paper establishes two infinite hierarchies of language families resulting from two variants of these automata. In addition, it demonstrates that these hierarchies coincide with the hierarchies resulting from parallel right linear grammars and right linear simple matrix grammars, so the self-regulating finite automata can be viewed as the automaton counterparts to these grammars. Finally, this paper compares both infinite hierarchies. In addition, as an open problem area, it suggests the discussion of self-regulating pushdown automata and points out that they give rise to no infinite hierarchy analogical to the achieved hierarchies resulting from the self-regulating finite automata.