The degree of word-expansion of lexicalized RRWW-automata - A new measure for the degree of nondeterminism of (context-free) languages

Authors:
F. Mráz;F. Otto;M. Plátek
Affiliations:
Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Malostranské nám. 25, 118 00 Praha 1, Czech Republic;Fachbereich Elektrotechnik/Informatik, Universität Kassel, 34109 Kassel, Germany;Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Malostranské nám. 25, 118 00 Praha 1, Czech Republic
Venue:
Theoretical Computer Science
Year:
2009

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Abstract

Restarting automata can be seen as analytical variants of classical automata as well as of regulated rewriting systems. We study a measure for the degree of nondeterminism of (context-free) languages in terms of deterministic restarting automata that are (strongly) lexicalized. This measure is based on the number of occurrences of auxiliary symbols (categories) used for recognizing a language as the projection of its characteristic language onto its input alphabet. This type of recognition is typical for analysis by reduction, a method used in linguistics for the creation and verification of formal descriptions of natural languages. Our main results establish a hierarchy of classes of context-free languages and two hierarchies of classes of non-context-free languages that are based on the expansion factor of a language.