Propositional SAT Solving

Marques-Silva, João; Malik, Sharad

doi:10.1007/978-3-319-10575-8_9

Cited by 17 publications

(7 citation statements)

References 50 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The first class is the full algorithms that are guaranteed to end with a right choice as to whether the CNF is satisfied or unsatisfied. DPLL and Clause Learning (CDCL) Conflict-Driven algorithms fall into the full algorithm category [26], [51], [21], [52,53,54,55]. The second class is incomplete schemes that don't give the assurance that a good satisfactory assignment will either be reported in a preset time limit or declared unsatisfactory, but a solution can be found quicker than a complete algorithm.…”

Section: A Boolean Satisfiability Issuementioning

confidence: 99%

An Effective SAT Solver Utilizing ACO Based on Heterogenous Systems

et al. 2020

View full text Add to dashboard Cite

This paper presents new parallel strategies for preprocessing and solving the issue of Boolean Satisfaction (SAT) on Heterogeneous systems of multicore and many-core CPU and Graphics Processing Unit (GPU) using Open Multi-Processor (OpenMP) and NVIDIA-CUDA. We propose exceptionally proficient and parallel techniques for SAT simplifications using the variable elimination method based on the Davis-Putnam-Logemann-Loveland (DPLL) slitting rule algorithm performed with a shared-memory model on a multicore CPU platform, where the clause elimination subsumption and the pure-literal removal techniques are completely performed on the CUDA framework. We demonstrate how efficient an evolutionary SAT solver is by using the suggested heterogeneous pre-processing, leading to important acceleration improvements in the solution's quality enhancement. The penalization of the transformative SAT solver is executed with Ant Colony Optimization (ACO) scheme utilizing CUDA. (Compute Unified Device Architecture) We perform thorough benchmarks to test the performance of our preprocessor and solver implementations against various random SAT formulas. The promoted H-SAT pre-processor scheme has gotten a speed-up of a factor 15x over the sequential implementation with statistical reductions on the original CNF which becomes up to 49% and 43% in case of literals and clauses numbers exclusively, where the H-SAT gain strength the solvability of the ACO solver by 100% in some cases.

show abstract

Section: A Boolean Satisfiability Issuementioning

confidence: 99%

An Effective SAT Solver Utilizing ACO Based on Heterogenous Systems

et al. 2020

View full text Add to dashboard Cite

show abstract

“…We use common notation for propositional logic and many-sorted first-order logic as can be reviewed in [2,22]. In particular, we define a signature as Σ = Σ S , Σ P , Σ F , ∫ P , ∫ F where Σ S are the available sorts, Σ P are the predicate symbols, Σ F are the function symbols and ∫ P : Σ P → Σ S * (∫ F : Σ F → Σ S + ) defines the rank of a given predicate (function).…”

Section: Preliminariesmentioning

confidence: 99%

An Incremental Abstraction Scheme for Solving Hard SMT-Instances over Bit-Vectors

Teuber¹,

Büning²,

Sinz³

2020

Preprint

View full text Add to dashboard Cite

Decision procedures for SMT problems based on the theory of bit-vectors are a fundamental component in state-of-the-art software and hardware verifiers. While very efficient in general, certain SMT instances are still challenging for state-of-the-art solvers (especially when such instances include computationally costly functions). In this work, we present an approach for the quantifier-free bit-vector theory (QF_BV in SMT-LIB) based on incremental SMT solving and abstraction refinement. We define four concrete approximation steps for the multiplication, division and remainder operators and combine them into an incremental abstraction scheme. We implement this scheme in a prototype extending the SMT solver Boolector and measure both the overall performance and the performance of the single approximation steps. The evaluation shows that our abstraction scheme contributes to solving more unsatisfiable benchmark instances, including seven instances with unknown status in SMT-LIB.

show abstract

“…Recently, one of the major motivations in proof complexity has been its close connection to SAT solving [ 29 , 54 ]. SAT solvers have turned into ubiquitous tools for the solution of hard computational problems from almost all application domains [ 46 ], yet a theoretical understanding of their effectiveness is only initially developed. The main approach comes through proof complexity.…”

Section: Introductionmentioning

confidence: 99%

Proof Complexity of Modal Resolution

Sigley

Beyersdorff

2021

J Autom Reasoning

View full text Add to dashboard Cite

We investigate the proof complexity of modal resolution systems developed by Nalon and Dixon (J Algorithms 62(3–4):117–134, 2007) and Nalon et al. (in: Automated reasoning with analytic Tableaux and related methods—24th international conference, (TABLEAUX’15), pp 185–200, 2015), which form the basis of modal theorem proving (Nalon et al., in: Proceedings of the twenty-sixth international joint conference on artificial intelligence (IJCAI’17), pp 4919–4923, 2017). We complement these calculi by a new tighter variant and show that proofs can be efficiently translated between all these variants, meaning that the calculi are equivalent from a proof complexity perspective. We then develop the first lower bound technique for modal resolution using Prover–Delayer games, which can be used to establish “genuine” modal lower bounds for size of dag-like modal resolution proofs. We illustrate the technique by devising a new modal pigeonhole principle, which we demonstrate to require exponential-size proofs in modal resolution. Finally, we compare modal resolution to the modal Frege systems of Hrubeš (Ann Pure Appl Log 157(2–3):194–205, 2009) and obtain a “genuinely” modal separation.

show abstract

Propositional SAT Solving

Cited by 17 publications

References 50 publications

An Effective SAT Solver Utilizing ACO Based on Heterogenous Systems

An Effective SAT Solver Utilizing ACO Based on Heterogenous Systems

An Incremental Abstraction Scheme for Solving Hard SMT-Instances over Bit-Vectors

Proof Complexity of Modal Resolution

Contact Info

Product

Resources

About