TY - GEN

T1 - Complexity of propositional proofs under a promise

AU - Dershowitz, Nachum

AU - Tzameret, Iddo

PY - 2007

Y1 - 2007

N2 - 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.

AB - 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.

KW - Promise problems

KW - Proof complexity

KW - Random 3CNF

KW - Resolution

UR - http://www.scopus.com/inward/record.url?scp=38149045780&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-73420-8_27

DO - 10.1007/978-3-540-73420-8_27

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AN - SCOPUS:38149045780

SN - 3540734198

SN - 9783540734192

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 291

EP - 302

BT - Automata, Languages and Programming - 34th International Colloquium, ICALP 2007, Proceedings

PB - Springer Verlag

T2 - 34th International Colloquium on Automata, Languages and Programming, ICALP 2007

Y2 - 9 July 2007 through 13 July 2007

ER -