Aligning CNF- and Equivalence-Reasoning

Heule, Marijn J. H.; Maaren, Hans van

doi:10.1007/11527695_12

Cited by 32 publications

(26 citation statements)

References 7 publications

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“…Related to this example, we note that in [25] XOR chains are explicitly detected on the CNF-level. Detected chains are removed if they contain a non-shared input gate (i.e., a variable that does not occur in the other clauses).…”

Section: Examplementioning

confidence: 56%

Simulating Circuit-Level Simplifications on CNF

2011

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Boolean satisfiability (SAT) and its extensions have become a core technology in many application domains, such as planning and formal verification, and continue finding various new application domains today. The SAT-based approach divides into three steps: encoding, preprocessing, and search. It is often argued that by encoding arbitrary Boolean formulas in conjunctive normal form (CNF), structural properties of the original problem are not reflected in the CNF. This should result in the fact that CNF-level preprocessing and SAT solver techniques have an inherent disadvantage compared to related techniques applicable on the level of more structural SAT instance representations such as Boolean circuits. Motivated by this, various simplification techniques and intricate CNF encodings for circuit-level SAT instance representations have been proposed. On the other hand, based on the highly efficient CNF-level clause learning SAT solvers, there is also strong support for the claim that CNF is sufficient as an input format for SAT solvers.In this work we study the effect of CNF-level simplification techniques, focusing on SatElite-style variable elimination (VE) and what we call blocked clause elimination (BCE). We show that BCE is surprisingly effective both in theory and in practice on CNF formulas resulting from a standard CNF encoding for circuits: without explicit knowledge of the underlying circuit structure, it achieves the same level of simplification as a combination of circuit-level simplifications and previously suggested polarity-based CNF encodings. We also show that VE can achieve many of the same effects as BCE, but not all. On the other hand, it turns out that VE and BCE are indeed partially orthogonal techniques. We also study 2 the practical effects of combining BCE and VE for reducing the size of formulas and on the running times of state-of-the-art SAT solvers. Furthermore, we address the problem of how to construct original witnesses to satisfiable CNF formulas when applying a combination of BCE and VE.

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Section: Examplementioning

confidence: 56%

Simulating Circuit-Level Simplifications on CNF

2011

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“…In [7] -appearing in the same volume -we propose a new look-ahead evaluation function for benchmarks containing equivalence clauses: let eq n be a weight for a reduced equivalence clause of new length n, C(x) the set of all reduced equivalence clauses (Q i ) during a look-ahead on x, and B(x) the set of all newly created binary clauses during the look-ahead on x. Using both sets, the lookahead evaluation can be calculated as in equation (2).…”

Section: Equivalence Reasoningmentioning

confidence: 99%

“…During our experiments, we used pre-selection heuristics which are an approximation of our combined look-ahead evaluation function (Ace) [7]. These pre-selection heuristics are costly, but because they provide a clear discrimination between the variables, a small subset of variables could be selected.…”

Section: Pre-selection Heuristicsmentioning

confidence: 99%

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March_eq: Implementing Additional Reasoning into an Efficient Look-Ahead SAT Solver

Heule

Dufour

Zwieten

et al. 2005

Theory and Applications of Satisfiability Testing

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Abstract. This paper discusses several techniques to make the lookahead architecture for satisfiability (Sat) solvers more competitive. Our contribution consists of reduction of the computational costs to perform look-ahead and a cheap integration of both equivalence reasoning and local learning. Most proposed techniques are illustrated with experimental results of their implementation in our solver march eq.

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“…Typical SAT solvers aimed at solving such structured problems are based on the CNF-level (clausal) Davis-Putnam-Logemann-Loveland procedure (DPLL) [1,2]. Research on boosting the efficiency of DPLL solvers has concentrated on incorporating techniques such as intelligent branching heuristics (e.g., [3][4][5]), novel propagation mechanisms (e.g., binary clause [6] and equivalence reasoning [7,8]), efficient propagator implementations (watched literals [5]), randomization and restarts [9,10], and clause learning [11].…”

Section: Introductionmentioning

confidence: 99%

The effect of structural branching on the efficiency of clause learning SAT solving: An experimental study

Järvisalo¹,

Niemelä²

2008

Journal of Algorithms

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Abstract. The techniques for making decisions, i.e., branching, play a central role in complete methods for solving structured instances of propositional satisfiability (SAT). Experimental case studies in specific problem domains have shown that in, some cases, SAT solvers benefit from structure-based limitations on which variables the solver is allowed to branch. Mainly, the focus has been on input (or independent) variables. Moreover, existing literature sheds little light on the effect of the restriction to the inner workings of SAT solvers, and in many cases current state-of-the-art solver techniques are not used. In this paper we present an extensive experimental evaluation on the effect of structure-based branching restrictions on the efficiency of solving structural SAT instances. The emphasis is on the interplay of structure-based branching restrictions and clause learning based search techniques found in most modern complete SAT solvers: (i) We investigate the effect of input-branching on the effectiveness of clause learning bound heuristics and conflict clauses. (ii) To study whether the robustness of input-restricted branching can be improved, we apply controlled schemes for allowing branching additionally on CNF variables other than inputs based on structural propertiessuch as the number of occurrences of sub-formulas-of non-clausal formulas.

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Aligning CNF- and Equivalence-Reasoning

Cited by 32 publications

References 7 publications

Simulating Circuit-Level Simplifications on CNF

Simulating Circuit-Level Simplifications on CNF

March_eq: Implementing Additional Reasoning into an Efficient Look-Ahead SAT Solver

The effect of structural branching on the efficiency of clause learning SAT solving: An experimental study

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