Satisfiability certificates verifiable in subexponential time

Evgeny Dantsin, Edward A. Hirsch

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


It is common to classify satisfiability problems by their time complexity. We consider another complexity measure, namely the length of certificates (witnesses). Our results show that there is a similarity between these two types of complexity if we deal with certificates verifiable in subexponential time. In particular, the well-known result by Impagliazzo and Paturi [IP01] on the dependence of the time complexity of k-SAT on k has its counterpart for the certificate complexity: we show that, assuming the exponential time hypothesis (ETH), the certificate complexity of k-SAT increases infinitely often as k grows. Another example of time-complexity results that can be translated into the certificate-complexity setting is the results of [CIP06] on the relationship between the complexity of k-SAT and the complexity of SAT restricted to formulas of constant clause density. We also consider the certificate complexity of CircuitSAT and observe that if CircuitSAT has subexponential-time verifiable certificates of length cn, where c < 1 is a constant and n is the number of inputs, then an unlikely collapse happens (in particular, ETH fails).

Original languageEnglish
Title of host publicationTheory and Application of Satisfiability Testing - 14th International Conference, SAT 2011, Proceedings
Number of pages14
StatePublished - 2011
Externally publishedYes
Event14th International Conference on Theory and Applications of Satisfiability Testing, SAT 2011 - Ann Arbor, MI, United States
Duration: 19 Jun 201122 Jun 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume6695 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Conference on Theory and Applications of Satisfiability Testing, SAT 2011
Country/TerritoryUnited States
CityAnn Arbor, MI


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