On the classes of languages accepted by limited context restarting automata^{∗,∗∗,∗∗∗}

¹ Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109 Kassel, Germany
otto@theory.informatik.uni-kassel.de
² Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Malostranské nám. 25, 11800 Praha 1, Czech Republic
petercerno@gmail.com; mraz@ksvi.ms.mff.cuni.cz

Received: 28 January 2013
Accepted: 8 January 2014

Abstract

In the literature various types of restarting automata have been studied that are based on contextual rewriting. A word w is accepted by such an automaton if, starting from the initial configuration that corresponds to input w, the word w is reduced to the empty word by a finite number of applications of these contextual rewritings. This approach is reminiscent of the notion of McNaughton families of languages. Here we put the aforementioned types of restarting automata into the context of McNaughton families of languages, relating the classes of languages accepted by these automata in particular to the class GCSL of growing context-sensitive languages and to the class CRL of Church–Rosser languages.