A Tutorial on Stålmarck’s Proof Procedure for Propositional Logic

Sheeran, Mary; Stålmarck, Gunnar

doi:10.1007/3-540-49519-3_7

Cited by 75 publications

(69 citation statements)

References 8 publications

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“…Stålmarck's Prover [23] has used this innovative approach successfully for testing satisfiability of many large-scale industrial problems. Such saturate-by-intersection methods proceed via iterative deepening.…”

Section: Intersection Methodsmentioning

confidence: 99%

“…In [23], all formulae are represented as definitional "triplets", of the form x ⇔ y ∧ z, where x, y, z are propositional variables, which is just the binomial x = yz in BR.…”

Section: Each Logical Gate F Is Associated With Two New Variables ν(mentioning

confidence: 99%

“…In Sect. 8, we apply the Boolean-ring representation in a framework-akin to Stålmarck's method [23] (see also [3]) and recursive learning [18]-that includes computing the intersection of sets of formulae. Preliminary experimental results may be found in Sect.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Boolean Rings for Intersection-Based Satisfiability

Dershowitz

Hsiang

Huang

et al. 2006

Logic for Programming, Artificial Intelligence, and Reasoning

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There is not a person in this courtroomwho has never told a lie, who has never done an immoral thing, and there is no man living who has never looked upon a woman without desire. 1 -Harper Lee: To Kill a MockingbirdAbstract. A potential advantage of using a Boolean-ring formalism for propositional formulae is the large measure of simplification it facilitates. We propose a combined linear and binomial representation for Booleanring polynomials with which one can easily apply Gaussian elimination and Horn-clause methods to advantage. We demonstrate that this framework, with its enhanced simplification, is especially amenable to intersection-based learning, as in recursive learning and the method of Stålmarck. Experiments support the idea that problem variables can be eliminated and search trees can be shrunk by incorporating learning in the form of Boolean-ring saturation.

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Section: Intersection Methodsmentioning

confidence: 99%

“…In [23], all formulae are represented as definitional "triplets", of the form x ⇔ y ∧ z, where x, y, z are propositional variables, which is just the binomial x = yz in BR.…”

Section: Each Logical Gate F Is Associated With Two New Variables ν(mentioning

confidence: 99%

See 1 more Smart Citation

Boolean Rings for Intersection-Based Satisfiability

Dershowitz

Hsiang

Huang

et al. 2006

Logic for Programming, Artificial Intelligence, and Reasoning

View full text Add to dashboard Cite

show abstract

“…It is an integral part of many algorithms for manipulating different data structures representing circuits [8,9,10,11,12].…”

Section: Structural Hashing On the Cnf-level Via Hbrmentioning

confidence: 99%

Revisiting Hyper Binary Resolution

Heule

Järvisalo

Biere

2013

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

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Abstract. This paper focuses on developing efficient inference techniques for improving conjunctive normal form (CNF) Boolean satisfiability (SAT) solvers. We analyze a variant of hyper binary resolution from various perspectives: We show that it can simulate the circuit-level technique of structural hashing and how it can be realized efficiently using so called tree-based lookahead. Experiments show that our implementation improves the performance of state-of-the-art CNFlevel SAT techniques on combinational equivalent checking instances.

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“…Unfortunately, standard non-normal form tableaux tend to be rather inefficient, as many of the refinements available to clausal procedures are hard to adapt. Typical cases in point are unit resolution, especially for propositional provers like the Davis-PutnamLogemann-Loveland (DPLL) procedure [7], the β c rules of the KE calculus [6], the application of 'result substitutions' in Stålmarcks Procedure [17], and hyper tableaux [2]. The common feature of these techniques is that they involve inferences between several formulae derived from the formula to be proved, either by using one formula to simplify another one, or-for hyper tableau-making tableau expansions depend on the presence of certain literals on a branch.…”

Section: Introductionmentioning

confidence: 99%