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.
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Mráz, F., Plátek, M., Otto, F. (2007). A Measure for the Degree of Nondeterminism of Context-Free Languages. In: Holub, J., Žďárek, J. (eds) Implementation and Application of Automata. CIAA 2007. Lecture Notes in Computer Science, vol 4783. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-76336-9_19
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DOI: https://doi.org/10.1007/978-3-540-76336-9_19
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