ReachFewL = ReachUL
We show that two complexity classes introduced about two decades ago are unconditionally equal. ReachUL is the class of problems decided by nondeterministic log-space machines which on every input have at most one computation path from the start configuration to any other configuration. ReachFewL, a natural generalization of ReachUL, is the class of problems decided by nondeterministic log-space machines which on every input have at most polynomially many computation paths from the start configuration to any other configuration. We show that ReachFewL = ReachUL.
KeywordsLog-space complexity unambiguous computations graph reachability
Subject classification68Q05 68Q10 68Q15 68Q17
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- Eric Allender, Klaus Reinhardt & Shiyu Zhou (1999). Isolation, Matching, and Counting Uniform and Nonuniform Upper Bounds. Journal of Computer and System Sciences 59(2), 164–181. ISSN 0022- 0000.Google Scholar
- Sanjeev Arora & Boaz Barak (2009). Computational Complexity - A Modern Approach. Cambridge University Press. ISBN 978-0-521- 42426-4.Google Scholar
- Chris Bourke, Raghunath Tewari, Vinodchandran N. V. (2009) Directed Planar Reachability Is in Unambiguous Log-Space. ACM Transactions on Computation Theory 1(1): 1–17Google Scholar
- Gerhard Buntrock, Birgit Jenner, Klaus-Jörn Lange & Peter Rossmanith (1991). Unambiguity and fewness for logarithmic space. In Proceedings of the 8th International Conference on Fundamentals of Computation Theory (FCT’91), Volume 529 Lecture Notes in Computer Science, 168–179. Springer-Verlag.Google Scholar
- Klaus-Jörn Lange (1997). An Unambiguous Class Possessing a Complete Set. In Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science (STACS’97), 339–350.Google Scholar
- A. Pavan, Raghunath Tewari & N. V. Vinodchandran (2010). On the Power of Unambiguity in Logspace To appear in Computational Complexity.Google Scholar
- Klaus Reinhardt & Eric Allender (2000). Making nondeterminism unambiguous. SIAM Journal on Computing 29(4), 1118 – 1131. ISSN 0097-5397.Google Scholar
- Thomas Thierauf & Fabian Wagner (2009). Reachability in K 3,3- Free Graphs and K 5-Free Graphs Is in Unambiguous Log-Space. In Proceedings of the 26th International Conference on Fundamentals of Computation Theory (FCT’09), 323–334.Google Scholar