Relationship between density and deterministic complexity of MP-complete languages

Piotr Berman

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

50 Scopus citations

Abstract

Let Σ be an arbitrary alphabet. denotes ɛ∪Σ∪..∪Σn. We say that a function t, t: is f-sparse iff card for every natural n. The main theorem of this paper establishes that if CLIQUE has some f-sparse translation into another set, which is calculable by a deterministic Turing machine in time bounded by f, then all the sets belonging to NP are calculable in time bounded by a function polynomially related to f. The proof is constructive and shows the way of constructing a proper algorithm. The simplest and most significant corollary says that if there is an NP-complete language over a single letter alphabet, then P=NP.

Original languageEnglish (US)
Title of host publicationAutomata, Languages and Programming - 5th Colloquium
EditorsCorrado Bohm, Giorgio Ausiello
PublisherSpringer Verlag
Pages63-71
Number of pages9
ISBN (Print)9783540088608
DOIs
StatePublished - 1978
Event5th International Colloquium on Automata, Languages and Programming, ICALP 1978 - Udine, Italy
Duration: Jul 17 1978Jul 21 1978

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume62 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th International Colloquium on Automata, Languages and Programming, ICALP 1978
CountryItaly
CityUdine
Period7/17/787/21/78

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Relationship between density and deterministic complexity of MP-complete languages'. Together they form a unique fingerprint.

Cite this