Quantitative relativizations of complexity classes
SIAM Journal on Computing
The Boolean hierarchy I: structural properties
SIAM Journal on Computing
A uniform approach to define complexity classes
Theoretical Computer Science
A taxonomy of complexity classes of functions
Journal of Computer and System Sciences
Functions computable with limited access to NP
Information Processing Letters
Computing Solutions Uniquely Collapses the Polynomial Hierarchy
SIAM Journal on Computing
The complexity of obtaining solutions for problems in NP and NL
Complexity theory retrospective II
A hierarchy based on output multiplicity
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
A note on parallel queries and the symmetric-difference hierarchy
Information Processing Letters
SIAM Journal on Computing
Subtractive Reductions and Complete Problems for Counting Complexity Classes
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
On NP-Partitions over Posets with an Application to Reducing the Set of Solutions of NP Problems
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Reducing the Number of Solutions of NP Functions
Reducing the Number of Solutions of NP Functions
Algebraic Properties for P-Selectivity
COCOON '01 Proceedings of the 7th Annual International Conference on Computing and Combinatorics
On NP-Partitions over Posets with an Application to Reducing the Set of Solutions of NP Problems
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
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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.