Abstract
The amount of nondeterminism that a pushdown automaton requires to recognize an input string can be measured by the minimum number of guesses that it must make to accept the string, where guesses are measured in bits of information. When this quantity is unbounded, the rate at which it grows as the length of the string increases serves as a measure of the pushdown automaton's “rate of consumption” of non-determinism. We show that this measure is similar to other complexity measures in that it gives rise to an infinite hierarchy of complexity classes of context-free languages differing in the amount of this resource (nondeterminism) that they require. In addition, we show that there are contextfree languages that can only be recognized by a pushdown automaton whose nondeterminism grows linearly, resolving an open problem in the literature. In particular, {ww R: wε {a,b}}*} is such a language.
This author's research was supported in part by the Stiftung Volkswagenwerk under Grant No. II/62 325.
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Aho, A., Ullman, J.: The Theory of Parsing, Translation, and Compiling. Prentice-Hall, Englewood Cliffs, NJ (1972)
Goldstine, J., Kintala, C., Wotschke, D.: On measuring nondeterminism in regular languages. Information and Computation 86 (1990) 179–194
Heilbrunner, S.: A parsing automata approach to LR theory. Theoretical Comp. Sci. 15 (1981) 117–157
Herzog, C.: Pushdown automata with bounded nondeterminism or bounded ambiguity. Proceedings LATIN '95, Lecture Notes in Computer Science 911 (1995) 358–370
Hopcroft, J., Ullman, J.: Introduction to Automata Theory, Languages, and Computation. Addison Wesley, Reading, MA (1979)
Kintala, C.: Refining nondeterminism in context-free languages. Math. Systems Theory 12 (1978) 1–8
Sippu, S., Soisalon-Soininen, E.: Parsing Theory. Springer-Verlag, Berlin (1988)
Salomaa, K., Yu, S.: Limited nondeterminism for pushdown automata. Bulletin of the EATCS 50 (1993) 186–193
Salomaa, K., Yu, S.: Measures of nondeterminism for pushdown automata. J. Comp. System Sci. 49 (1994) 362–374
Vermeir, D., Savitch, W.: On the amount of nondeterminism in pushdown automata. Fundamenta Informaticae 4 (1981) 401–418
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© 1997 Springer-Verlag Berlin Heidelberg
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Goldstine, J., Leung, H., Wotschke, D. (1997). Measuring nondeterminism in pushdown automata. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023467
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DOI: https://doi.org/10.1007/BFb0023467
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