Computing solutions uniquely collapses the polynomial hierarchy

Lane A. Hemaspaandra, Ashish V. Naik, Mitsunori Ogihara, Alan L. Selman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations


We show that if there is an NP function that, when given a satisfiable formula as input, outputs one satisfying assignment uniquely, then the polynomial hierarchy collapses to its second level. As the existence of such a function is known to be equivalent to the statement “every NP function has an NP refinement with unique outputs,” our result provides the strongest evidence yet that NP functions cannot be refined.

Original languageEnglish (US)
Title of host publicationAlgorithms and Computation - 5th International Symposium, ISAAC 1994, Proceedings
EditorsDing-Zhu Du, Ding-Zhu Du, Xiang-Sun Zhang
PublisherSpringer Verlag
Number of pages8
ISBN (Print)9783540583257
StatePublished - 1994
Externally publishedYes
Event5th Annual International Symposium on Algorithms and Computation, ISAAC 1994 - Beijing, China
Duration: Aug 25 1994Aug 27 1994

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume834 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other5th Annual International Symposium on Algorithms and Computation, ISAAC 1994

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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