Degrees of non-monotonicity for restarting automata

Authors:
T. Jurdziński;F. Mráz;F. Otto;M. Plátek
Affiliations:
Institute of Computer Science, University of Wrocław, Wrocław, Poland;Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Praha I, Czech Republic;Fachbereich Mathematik/Informatik, Universität Kassel, Kassel, Germany;Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Praha I, Czech Republic
Venue:
Theoretical Computer Science
Year:
2006

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Abstract

In the literature various notions of monotonicity for restarting automata have been studied. Here we introduce two new variants of monotonicity for restarting automata and for two-way restarting automata: left-monotonicity and right-left-monotonicity. It is shown that for the various types of deterministic and nondeterministic (two-way) restarting automata without auxiliary symbols, these notions yield infinite hierarchies, and we compare these hierarchies to each other. Further, as a tool used to simplify some of the proofs, the shrinking restarting automaton is introduced, which is a generalization of the standard (length-reducing) restarting automaton to the weight-reducing case. Some of the consequences of this generalization are also discussed.