Journal of Computer and System Sciences - Special issue: 26th annual ACM symposium on the theory of computing & STOC'94, May 23–25, 1994, and second annual Europe an conference on computational learning theory (EuroCOLT'95), March 13–15, 1995
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
The Efficiency of Resolution and Davis--Putnam Procedures
SIAM Journal on Computing
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Pseudorandom Generators in Propositional Proof Complexity
SIAM Journal on Computing
Witnesses for non-satisfiability of dense random 3CNF formulas
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Substitutions into propositional tautologies
Information Processing Letters
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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 Λ in the number of variables n. To this end, we develop propositional proof systems under different measures of promises (i.e., 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: (1) Resolution has polynomial-size refutations for all unsatisfiable 3CNF formulas when the promise is &epsis;⋅2n, for any constant 0 (2) There are no subexponential size resolution refutations for random 3CNF formulas, when the promise is 2δ n, for any constant 0O(n3/2−&epsis;), for 0 “Goods Satisfactory or Money Refunded” —The Eaton Promise