Reducing the number of solutions of NP functions

Lane A. Hemaspaandra, Mitsunori Ogihara, Gerd Wechsung

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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, 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.

Original languageEnglish (US)
Pages (from-to)311-328
Number of pages18
JournalJournal of Computer and System Sciences
Issue number2
StatePublished - Mar 2002
Externally publishedYes


  • Cardinality types
  • Computational complexity
  • Function refinement
  • Multivalued functions
  • NP functions
  • NPMV
  • Reducing solutions
  • Selectivity theory
  • Semi-feasible computation
  • Solution-pruning algorithms
  • The Narrowing-Gap Condition

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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