On restarting automata with auxiliary symbols and small window size^*

¹ Charles University, Faculty of Mathematics and Physics, Malostranské nám. 25, 118 25 Prague 1, Czech Republic.
² Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109 Kassel, Germany.

^** Corresponding author: f.otto@uni-kassel.de

Received: 6 December 2019
Accepted: 29 April 2021

Abstract

Here we show that for monotone RWW- (and RRWW-) automata, window size two is sufficient, both in the nondeterministic as well as in the deterministic case. For the former case, this is done by proving that each context-free language is already accepted by a monotone RWW-automaton of window size two. In the deterministic case, we first prove that each deterministic pushdown automaton can be simulated by a deterministic monotone RWW-automaton of window size three, and then we present a construction that transforms a deterministic monotone RWW-automaton of window size three into an equivalent automaton of the same type that has window size two. Furthermore, we study the expressive power of shrinking RWW- and RRWW-automata the window size of which is just one or two. We show that for shrinking RRWW-automata that are nondeterministic, window size one suffices, while for nondeterministic shrinking RWW-automata, we already need window size two to accept all growing context-sensitive languages. In the deterministic case, shrinking RWW- and RRWW-automata of window size one accept only regular languages, while those of window size two characterize the Church-Rosser languages.