On the Circuit Complexity of Random Generation Problems for Regular and Context-Free Languages
We study the circuit complexity of generating at random a word of length n from a given language under uniform distribution. We prove that, for every language accepted in polynomial time by 1-NAuxPDA of polynomially bounded ambiguity, the problem is solvable by a logspace-uniform family of probabilistic boolean circuits of polynomial size and O(log2 n) depth. Using a suitable notion of reducibility (similar to the NC1-reducibility), we also show the relationship between random generation problems for regular and context-free languages and classical computational complexity classes such as DIV, L and DET.
KeywordsUniform random generation ambiguous context-free languages auxiliary pushdown automata circuit complexity
Unable to display preview. Download preview PDF.
- A. Bertoni, M. Goldwurm, and M. Santini. Random generation and approximate counting of ambiguously described combinatorial structures. In Horst Reichel and Sophie Tison, editors, Proceedings of 17th Annual Symposium on Theoretical Aspects of Computer Science (STACS), number 1770 in Lecture Notes in Computer Science, pages 567–580. Springer, 2000.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
- R. M. Karp and V. Ramachandran. Parallel algorithms for shared-memory machines. In J. van Leeuwen, editor, Handbook of Computer Science. MIT Press/Elsevier, 1992.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
- D. B. Searls. The computational linguistics of biological sequences. In Larry Hunter, editor, Artificial Intelligence and Molecular Biology, chapter 2, pages 47–120. AAAI Press, 1992.Google Scholar
- R. Smith. A finite state machine algorithm for finding restriction sites and other pattern matching applications. Comput. Appl. Biosci., 4:459–465, 1988.Google Scholar
- V. Vinay. Counting auxiliary pushdown automata and semi-unbounded arithmetic circuits. In Christopher Balcázar, José; Borodin, Alan; Gasarch, Bill; Immerman, Neil; Papadimitriou, Christos; Ruzzo, Walter; Vitányi, Paul; Wilson, editor, Proceedings of the 6th Annual Conference on Structure in Complexity Theory (SCTC’ 91), pages 270–284, Chicago, IL, USA, June 1991. IEEE Computer Society Press.Google Scholar