On-the-Fly Clause Improvement

Han, Hyojung; Somenzi, Fabio

doi:10.1007/978-3-642-02777-2_21

Cited by 32 publications

(19 citation statements)

References 7 publications

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“…Notice also that, similar to on-the-fly self-subsuming resolution [24], BCE can also be applied on-the-fly during VE. If elimination of a candidate variable would add too many resolvents and the variable is not eliminated, some of the antecedents could still have produced only tautologies.…”

Section: Some Practical Aspectsmentioning

confidence: 99%

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: Some Practical Aspectsmentioning

confidence: 99%

Simulating Circuit-Level Simplifications on CNF

2011

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“…In this architecture, if the original CNF formula is simplified, then all processes can benefit from those simplifications. For example, if one process detects a clause for "on-the-fly improvement" [46], then all processes may profit from this immediately. This architecture has been implemented in the past in ySAT [29] and more recently in SArTagnan [54].…”

Section: Solver Architecturementioning

confidence: 99%

An overview of parallel SAT solving

2012

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“…If C = l ∨ C and C = ¬l ∨ D, where l is a literal, and C and D are disjunction of literals with D ⊆ C, the resolvent of C and C is C and subsumes C , meaning that l is redundant in C and can be removed from C . This approach allows to minimize both original and learnt clauses during the search and was proposed independently in [10] and [11]. It was implemented in CryptoMinisat 2.5.0 [39] for on-the-fly clause improvement.…”

Section: Related Work On Elimination Of Redundant Literalsmentioning

confidence: 99%

Clause vivification by unit propagation in CDCL SAT solvers

Xiao

Luo

et al. 2020

Artificial Intelligence

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Original and learnt clauses in Conflict-Driven Clause Learning (CDCL) SAT solvers often contain redundant literals. This may have a negative impact on performance because redundant literals may deteriorate both the effectiveness of Boolean constraint propagation and the quality of subsequent learnt clauses. To overcome this drawback, we propose a clause vivification approach that eliminates redundant literals by applying unit propagation. The proposed clause vivification is activated before the SAT solver triggers some selected restarts, and only affects a subset of original and learnt clauses, which are considered to be more relevant according to metrics like the literal block distance (LBD). Moreover, we conducted an empirical investigation with instances coming from the hard combinatorial and application categories of recent SAT competitions. The results show that a remarkable number of additional instances are solved when the proposed approach is incorporated into five of the best performing CDCL SAT solvers (Glucose, TC Glucose, COMiniSatPS, MapleCOMSPS and MapleCOMSPS LRB). More importantly, the empirical investigation includes an in-depth analysis of the effectiveness of clause vivification. It is worth mentioning that one of the SAT solvers described here was ranked first in the main track of SAT Competition 2017 thanks to the incorporation of the proposed clause vivification. That solver was further improved in this paper and won the bronze medal in the main track of SAT Competition 2018.

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On-the-Fly Clause Improvement

Cited by 32 publications

References 7 publications

Simulating Circuit-Level Simplifications on CNF

Simulating Circuit-Level Simplifications on CNF

An overview of parallel SAT solving

Clause vivification by unit propagation in CDCL SAT solvers

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