Improved Conflict-Clause Minimization Leads to Improved Propositional Proof Traces

Gelder, Allen Van

doi:10.1007/978-3-642-02777-2_15

Cited by 11 publications

(14 citation statements)

References 6 publications

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“…Additional experiments (whose results we do not detail for space constraints) show that deletion of clauses alone is responsible for a speedup of more than one order of magnitude for the larger instances, when using the certified checker we develop in the next section. While it is in principle thinkable to modify a SAT solver to output the GRIT format directly, building on [38], in this work our focus is on enabling sufficiently efficient certified proof checking. To this end, it seems fully acceptable to run an uncertified proof checker as a pre-processor to generate the oracle data enabling the application of restricted reverse unit propagation in a certified checker.…”

Section: The Checkermentioning

confidence: 99%

Efficient Certified Resolution Proof Checking

Cruz-Filipe

Marques-Silva

Schneider–Kamp

2017

Lecture Notes in Computer Science

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Abstract. We present a novel propositional proof tracing format that eliminates complex processing, thus enabling efficient (formal) proof checking. The benefits of this format are demonstrated by implementing a proof checker in C, which outperforms a state-of-the-art checker by two orders of magnitude. We then formalize the theory underlying propositional proof checking in Coq, and extract a correct-by-construction proof checker for our format from the formalization. An empirical evaluation using 280 unsatisfiable instances from the 2015 and 2016 SAT competitions shows that this certified checker usually performs comparably to a state-of-the-art non-certified proof checker. Using this format, we formally verify the recent 200 TB proof of the Boolean Pythagorean Triples conjecture.

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Section: The Checkermentioning

confidence: 99%

Efficient Certified Resolution Proof Checking

Cruz-Filipe

Marques-Silva

Schneider–Kamp

2017

Lecture Notes in Computer Science

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“…For propositional conflict-driven clause learning, it is known that the learned clause has a quadratically long derivation, in terms of the overall number of clauses needed to derive it, even when clause minimization and "volunteers" are included [23,24]. (See cited papers; minimization and volunteers are not important to this paper.)…”

Section: Qu-resolutionmentioning

confidence: 99%

Contributions to the Theory of Practical Quantified Boolean Formula Solving

Gelder

2012

Lecture Notes in Computer Science

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Abstract. Recent solvers for quantified boolean formulas (QBFs) use a clause learning method based on a procedure proposed by Giunchiglia et al. (JAIR 2006), which avoids creating tautological clauses. The underlying proof system is Q-resolution. This paper shows an exponential worst case for the clause-learning procedure. This finding confirms empirical observations that some formulas take mysteriously long times to solve, compared to other apparently similar formulas. Q-resolution is known to be refutation complete for QBF, but not all logically implied clauses can be derived with it. A stronger proof system called QU-resolution is introduced, and shown to be complete in this stronger sense. A new procedure called QPUP for clause learning without tautologies is also described. A generalization of pure literals is introduced, called effectively depthmonotonic literals. In general, the variable-elimination resolution operation, as used by Quantor, sQueezeBF, and Bloqqer is unsound if the existential variable being eliminated is not at innermost scope. It is shown that variable-elimination resolution is sound for effectively depthmonotonic literals even when they are not at innermost scope.

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“…Then it is a "folklore theorem" that this problem can be solved in P-time and that the minimum-width clause is unique [16,17]. The procedure implemented in MiniSat 2.0 [8] is believed to achieve this.…”

Section: Conflict-clause Strengthening Problemmentioning

confidence: 99%

“…The method used in MiniSat 2.0 amounts to doing additional resolutions (possibly redundantly) on literals that were implied in earlier propagation sequences, yielding a subset of the original conflict clause [8,16]. It is now known that the redundancy is efficiently avoidable [17]. Volunteer clauses are not used.…”

Section: Implication Sequences and Linear Input Regular Derivationsmentioning

confidence: 99%

“…In recent papers two rather surprising observations have emerged concerning solution of typical industrial instances, with thousands of variables and over a million clauses, in some cases: (1) conflict clauses can be reduced 32% in width, on average, permitting a substantial savings in memory [2]; (2) these reductions can be discovered and applied to achieve substantial net savings in time, as well [16,17]. the method sketched in a poster by Sörensson and Eén, The reduction method has come to be known as recursive conflict-clause minimization.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Conflict-Clause Strengthening for Satisfiability Solvers

Gelder

2011

Theory and Applications of Satisfiability Testing - SAT 2011

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Abstract. The dominant propositional satisfiability solvers of the past decade use a technique often called conflict-driven clause learning (cdcl), although nomenclature varies. The first half of the decade concentrated on deriving the best clause from the conflict graph that the technique constructs, also with much emphasis on speed. In the second half of the decade efforts have emerged to exploit other information that is derived by the technique as a by-product of generating the conflict graph and learning a conflict clause. The main thrust has been to strengthen the conflict clause by eliminating some of its literals, a process often called conflict-clause minimization, but more accurately described as conflictclause width reduction, or strengthening. This paper first introduces implication sequences as a general framework to represent all the information derived by the CDCL technique, some of which is not represented in the conflict graph. Then the paper analyzes the structure of this information. The first main result is that any conflict clause that is a logical consequence of an implication sequence may be derived by a particularly simple form of resolution, known as linear input regular. A key observation needed for this result is that the set of clauses in any implication sequence is Horn-renamable. The second main result is that, given an implication sequence, and a clause C derived (learned) from it, it is NP -hard to find a minimum-cardinality subset of C that is also derivable. This is in sharp contrast to the known fact that such a minimum subset can be found quickly if the derivation is restricted to using only clauses in the conflict graph.

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Improved Conflict-Clause Minimization Leads to Improved Propositional Proof Traces

Cited by 11 publications

References 6 publications

Efficient Certified Resolution Proof Checking

Efficient Certified Resolution Proof Checking

Contributions to the Theory of Practical Quantified Boolean Formula Solving

Generalized Conflict-Clause Strengthening for Satisfiability Solvers

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