Almost complete sets

Klaus Ambos-Spies, Wolfgang Merkle, Jan Severin Reimann, Sebastiaan A. Terwijn

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

1 Scopus citations

Abstract

We show that there is a set which is almost complete but not complete under polynomial-time many-one (p-m) reductions for the class E of sets computable in deterministic time 2lin. Here a set A in a complexity class C is almost complete for C under some reducibility r if the class of the problems in C which do not r-reduce to A has measure 0 in C in the sense of Lutz's resource-bounded measure theory. We also show that the almost complete sets for E under polynomial-time bounded one-one length-increasing reductions and truth-table reductions of norm 1 coincide with the almost p-m-complete sets for E. Moreover, we obtain similar results for the class EXP of sets computable in deterministic time 2poly.

Original languageEnglish (US)
Title of host publicationSTACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings
PublisherSpringer Verlag
Pages419-430
Number of pages12
ISBN (Print)9783540671411
StatePublished - Jan 1 2000
Event17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000 - Lille, France
Duration: Feb 17 2000Feb 19 2000

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1770
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000
CountryFrance
CityLille
Period2/17/002/19/00

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Ambos-Spies, K., Merkle, W., Reimann, J. S., & Terwijn, S. A. (2000). Almost complete sets. In STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings (pp. 419-430). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1770). Springer Verlag.