Abstract
We study whether one can prune solutions from NP functions. Though it is known that, unless surprising complexity class collapses occur, one cannot reduce the number of accepting paths of NP machines [17], we nonetheless show that it often is possible to reduce the number of solutions of NP functions. For finite cardinality types, we give a sufficient condition for such solution reduction. We also give absolute and conditional necessary conditions for solution reduction, and in particular we show that in many cases solution reduction is impossible unless the polynomial hierarchy collapses.
Supported in part by grants DARPA-F30602-98-2-0133, NSF-CCR-9701911, NSF-INT-9726724, and NSF-INT-9815095/DAAD-315-PPP-gü-ab. Work done in part while the first author was visiting Friedrich-Schiller-Universität Jena and Julius-Maximilians-Universität Würzburg, and while the third author was visiting RIT.
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Hemaspaandra, L.A., Ogihara, M., Wechsung, G. (2000). Reducing the Number of Solutions of NP Functions. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_35
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DOI: https://doi.org/10.1007/3-540-44612-5_35
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