Abstract of Paper |

*Reducing the Number of Solutions of NP Functions*

by Lane Hemaspaandra, Mitsunori Ogihara, and Gerd Wechsung

**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 (Ogihara, M., and Hemachandra, L.A., Journal of Computer and System Sciences, volume 46, pages 295--325, 1993), 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.