2007 | OriginalPaper | Buchkapitel
Complexity of Propositional Proofs Under a Promise
verfasst von : Nachum Dershowitz, Iddo Tzameret
Erschienen in: Automata, Languages and Programming
Verlag: Springer Berlin Heidelberg
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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 (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
.2
n
, for any constant 0 <
ε
< 1.
(ii) There are no sub-exponential size resolution refutations for random 3CNF formulas, when the promise is 2
δn
(and the number of clauses is
o
(
n
3/2
)), for any constant 0 <
δ
< 1.