This chapter defines and investigates self-regulating automata. They regulate the selection of a rule according to which the current move is made by a rule according to which a previous move was made. Both finite and pushdown versions of these automata are investigated. The chapter is divided into two sections. Section 15.1 discusses self-regulating finite automata. It establishes two infinite hierarchies of language families resulting from them. Both hierarchies lie between the family of regular languages and the family of context-sensitive languages. Section 15.2 studies self-regulating pushdown automata. Based upon them, this section characterizes the families of context-free and recursively enumerable languages. However, as opposed to the results about self-regulating finite automata, many questions concerning their pushdown versions remain open; indeed, Sect. 15.2 formulates several specific open problem areas, including questions concerning infinite language-family hierarchies resulting from them.
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