Isolation, Matching, and Counting: Uniform and Nonuniform Upper Bounds (1998)
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| Venue: | Journal of Computer and System Sciences |
| Citations: | 17 - 4 self |
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@ARTICLE{Allender98isolation,matching,,
author = {Eric Allender and Klaus Reinhardt and Shiyu Zhon},
title = {Isolation, Matching, and Counting: Uniform and Nonuniform Upper Bounds},
journal = {Journal of Computer and System Sciences},
year = {1998},
volume = {59},
pages = {181}
}
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Abstract
We show that the perfect matching problem is in the complexity class SPL (in the nonuniform setting). This provides a better upper bound on the complexity of the matching problem, as well as providing motivation for studying the complexity class SPL. Using similar techniques, we show that counting the number of accepting paths of a nondeterministic logspace machine can be done in NL/poly, if the number of paths is small. This clarifies the complexity of the class LogFew (defined and studied in [BDHM91]). Using derandomization techniques, we then improve this to show that this counting problem is in NL. Determining if our other theorems hold in the uniform setting remains an The material in this paper appeared in preliminary form in papers in the Proceedings of the IEEE Conference on Computational Complexity, 1998, and in the Proceedings of the Workshop on Randomized Algorithms, Brno, 1998. y Supported in part by NSF grants CCR-9509603 and CCR-9734918. z Supported in part by the ...
