Complexity of propositional proofs under a promise

Nachum Dershowitz*, Iddo Tzameret

*Corresponding author for this work

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


We study - within the framework of propositional proof complexity - the problem of certifying unsatisfiability of CNF formulas under the promise that any satisfiable formula has many satisfying assignments, where "many" stands for an explicitly specified function A in the number of variables n. To this end, we develop propositional proof systems under different measures of promises (that is, different Λ) as extensions of resolution. This is done by augmenting resolution with axioms that, roughly, can eliminate sets of truth assignments defined by Boolean circuits. We then investigate the complexity of such systems, obtaining an exponential separation in the average-case between resolution under different size promises: (i) Resolution has polynomial-size refutations for all unsatisfiable 3CNF formulas when the promise is ε·2n, for any constant 0 < ε < 1. (ii) There are no sub-exponential size resolution refutations for random 3CNF formulas, when the promise is 2δn (and the number of clauses is o(n 3/2)), for any constant 0 < 6 < 1.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)3540734198, 9783540734192
StatePublished - 2007
Event34th International Colloquium on Automata, Languages and Programming, ICALP 2007 - Wroclaw, Poland
Duration: 9 Jul 200713 Jul 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4596 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference34th International Colloquium on Automata, Languages and Programming, ICALP 2007


  • Promise problems
  • Proof complexity
  • Random 3CNF
  • Resolution


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