A measure for the degree of nondeterminism of context-free languages

Authors:
František Mráz;Martin Plátek;Friedrich Otto
Affiliations:
Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Praha 1, Czech Republic;Charles University, Faculty of Mathematics and Physics, Department of Computer Science, Praha 1, Czech Republic;Fachbereich Elektrotechnik/Informatik, Universität Kassel, Kassel, Germany
Venue:
CIAA'07 Proceedings of the 12th international conference on Implementation and application of automata
Year:
2007

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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 some measures for the degree of nondeterminism of (context-free) languages in terms of lexicalized deterministic restarting automata. These measures are based on the number 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 two-dimensional hierarchy of classes of (context-free) languages based on the expansion factor of a language and on the number of different auxiliary symbols available in the underlying characteristic language.