Faster SAT solving with better CNF generation

Chambers,; Manolios,; Vroon,

doi:10.1109/date.2009.5090918

Cited by 15 publications

(18 citation statements)

References 7 publications

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“…We encoded these 4379 structural SAT instances with four algorithms: the standard Tseitin encoding [47], the Plaisted-Greenbaum polarity-based encoding [43], the Minicirc encoder based on technology mapping [20] and VE, and the most recent NiceDAG encoder [40,13]. The NiceDAG implementation was obtained from the authors.…”

Section: Results On Achieved Simplificationsmentioning

confidence: 99%

“…To accompany the more theoretical analysis in this paper, we present an experimental evaluation of the effectiveness of BCE combined with SatElite-style variable eliminating CNF preprocessing comparing our implementation with the standard Tseitin and PlaistedGreenbaum encodings and the more recent NiceDAG [40,13] and Minicirc [20] CNF encoders. It turns out that the combination of these CNF-level techniques is in many cases competitive with the circuit-level encoders.…”

Section: Contributionsmentioning

confidence: 99%

“…The remaining 3672 SMT problems were bit-blasted to And-Inverter Graphs (AIGs) in the AIGER format (http://fmv.jku.at/aiger) using our SMT solver Boolector [10]. Furthermore, we used the AIG instances used in [13], consisting of two types of instances: (i) AIGs representing BMC problems (with step bound k = 45) obtained from all the 645 sequential HWMCC'08 (http://fmv.jku.at/hwmcc08) model checking problems, and (ii) 62 AIGs from the structural SAT track of the SAT competition. We have made the SMT-Lib instances publicly available at http://fmv.jku.at/aiger/ smtqfbv-aigs.7z (260MB); the others cannot be distributed due to license restrictions.…”

Section: Experiments Setupmentioning

confidence: 99%

“…Such circuit representations are typically afterwards automatically translated (encoded) into CNF for applying a CNF-level SAT solver to determine satisfiability of the formula. Various simplification techniques and intricate CNF encoders for general propositional formulas and especially circuit-level SAT instance representations have been proposed; see [43,8,28,41,20,40,13] for examples.…”

Section: Introductionmentioning

confidence: 99%

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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: Results On Achieved Simplificationsmentioning

confidence: 99%

Section: Contributionsmentioning

confidence: 99%

Section: Experiments Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simulating Circuit-Level Simplifications on CNF

2011

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“…Reducing the size of the CNF encodings derived from SAT formulas has been shown to be an effective way of optimizing SAT solvers [25,16,33,24,44,55]. There has been a lot of work on optimal encodings for specific kinds of constraints like cardinality constraints [1], sequence constraints [14], verification of microprocessors [55].…”

Section: Reducing Encodings Sizementioning

confidence: 99%

Synthesis of Domain Specific CNF Encoders for Bit-Vector Solvers

Inala

Singh

Solar-Lezama

2016

Theory and Applications of Satisfiability Testing – SAT 2016

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SMT solvers are at the heart of a number of software engineering tools. These SMT solvers use a SAT solver as the back-end and convert the high-level constraints given by the user down to low-level boolean formulas that can be efficiently mapped to CNF clauses and fed into a SAT solver. Current SMT solvers are designed to be general purpose solvers that are suited to a wide range of problems. However, SAT solvers are very non-deterministic and hence, it is difficult to optimize a general purpose solver across all different problems. In this thesis, we propose a system that can automatically generate parts of SMT solvers in a way that is tailored to particular problem domains. In particular, we target the translation from high-level constraints to CNF clauses which is one of the crucial parts of all SMT solvers. We achieve this goal by using a combination of program synthesis and machine learning techniques. We use a program synthesis tool called Sketch to generate optimal encoding rules for this translation and then use auto-tuning to only select the subset of these encodings that actually improve the performance for a particular class of problems.Using this technique, the thesis shows that we can improve upon the basic encoding strategy used by CVC4 (a state of the art SMT solver). We can automatically generate variants of the solver tailored to different domains of problems represented in the bit-vector benchmark suite from the SMT competition 2015.

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Reasoning with Propositional Logic: From SAT Solvers to Knowledge Compilation

Simon

2020

A Guided Tour of Artificial Intelligence Research

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Faster SAT solving with better CNF generation

Cited by 15 publications

References 7 publications

Simulating Circuit-Level Simplifications on CNF

Simulating Circuit-Level Simplifications on CNF

Synthesis of Domain Specific CNF Encoders for Bit-Vector Solvers

Reasoning with Propositional Logic: From SAT Solvers to Knowledge Compilation

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