Almost complete sets

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

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

1 Citation (Scopus)

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

Fingerprint

Polynomials
Polynomial time
Truth table
Measure Theory
Complexity Classes
Reducibility
Norm
Resources
Class

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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.
Ambos-Spies, Klaus ; Merkle, Wolfgang ; Reimann, Jan Severin ; Terwijn, Sebastiaan A. / Almost complete sets. STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings. Springer Verlag, 2000. pp. 419-430 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Ambos-Spies, K, Merkle, W, Reimann, JS & Terwijn, SA 2000, Almost complete sets. in STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1770, Springer Verlag, pp. 419-430, 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Lille, France, 2/17/00.

Almost complete sets. / Ambos-Spies, Klaus; Merkle, Wolfgang; Reimann, Jan Severin; Terwijn, Sebastiaan A.

STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings. Springer Verlag, 2000. p. 419-430 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1770).

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

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Ambos-Spies K, Merkle W, Reimann JS, Terwijn SA. Almost complete sets. In STACS 2000 - 17th Annual Symposium on Theoretical Aspects of Computer Science, STACS 2000, Proceedings. Springer Verlag. 2000. p. 419-430. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).