Recording the use of memory in right-boundary grammars and push-down automata (Q1099636)

The paper deals with the notion of coordinated selective substitution system, introduced by the third author [Theor. Comput. Sci. 37, 31-50 (1985; Zbl 0601.68054)] in the aim of obtaining a unified framework for studiyng various types of grammars and automata. The authors' abstract: ``Within the framework of coordinated pair systems a push-down automaton A is formalized as an ordered pair \((G_ 1,G_ 2)\) of grammars, where \(G_ 1\) is a right-linear grammar modelling the finite state control of A and the reading of the input of A, and \(G_ 2\) is a right-boundary grammar modelling the push-down store of A. In this paper we present a systematic investigation into the use of memory of right-boundary grammars. Various methods of recording the use of memory are introduced. The results presented concern regularity properties of each of the methods and the interrelationships of the records obtained by different methods. Finally the translation of these results to the level of push-down automata (coordinated pair systems) is discussed.'' Thus, the paper is a direct continuation (and ``together provides a rather complete picture of the use of memory in right-boundary grammars and in coordinating pair systems'') of a paper by the same authors, ibid. 48, 201-228 (1986; see the following review).