Random Generation and Approximate Counting of Ambiguously Described Combinatorial Structures
This paper concerns the uniform random generation and the approximate counting of combinatorial structures admitting an ambiguous description. We propose a general framework to study the complexity of these problems and present some applications to specific classes of languages. In particular, we give a uniform random generation algorithm for finitely ambiguous context-free languages of the same time complexity of the best known algorithm for the unambiguous case. Other applications include a polynomial time uniform random generator and approximation scheme for the census function of (i) languages recognized in polynomial time by one-way nondeterministic auxiliary pushdown automata of polynomial ambiguity and (ii) polynomially ambiguous rational trace languages.
Keywordsuniform random generation approximate counting context-free languages auxiliary pushdown automata rational trace languages inherent ambiguity
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- A. V. Aho and J. D. Ullman. The Theory of Parsing, Translation and Compiling-Vol.I: Parsing. Prentice Hall, Englewood Cliffs, NJ, 1972.Google Scholar
- A. Bertoni, M. Goldwurm, G. Mauri, and N. Sabadini. Counting techniques for inclusion, equivalence and membership problems. In V. Diekert and G. Rozenberg, editors, The Book of Traces, chapter 5, pages 131–164. World Scientific, Singapore, 1995.Google Scholar
- F.-J. Brandenburg. On one-way auxiliary pushdown automata. In H. Waldschmidt H. Tzschach and H. K.-G. Walter, editors, Proceedings of the 3rd GI Conference on Theoretical Computer Science, volume 48 of Lecture Notes in Computer Science, pages 132–144, Darmstadt, FRG, March 1977. Springer.Google Scholar
- V. Diekert and Y. Métivier. Partial commutation and traces. In G. Rozenberg and A. Salomaa, editors, Handbook on Formal Languages, volume III, pages 457–527. Springer, Berlin-Heidelberg, 1997.Google Scholar
- V. Diekert and G. Rozenberg. The Book of Traces. World Scientific, Singapore, 1995.Google Scholar
- P. Flajolet. Mathematical methods in the analysis of algorithms and data structures. In Egon Börger, editor, Trends in Theoretical Computer Science, chapter 6, pages 225–304. Computer Science Press, Rockville, Maryland, 1988.Google Scholar
- J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Language, and Computation. Addison-Wesley, Reading, MA, 1979.Google Scholar
- D. E. Knuth and A. C. Yao. The complexity of nonuniform random number generation. In J. F. Traub, editor, Algorithms and Complexity: New Directions and Recent Results, pages 357–428. Academic Press, 1976.Google Scholar
- C. Lautemann. On pushdown and small tape. In K. Wagener, editor, Dirk-Siefkes, zum 50. Geburststag (proceedings of a meeting honoring Dirk Siefkes on his fiftieth birthday), pages 42–47. Technische Universität Berlin and Universität Ausgburg, 1988.Google Scholar
- M. Santini. Random Uniform Generation and Approximate Counting of Combinatorial Structures. PhD thesis, Dipartimento di Scienze dell’Informazione — Università degli Studi di Milano, 1999.Google Scholar