Applying computer algebra systems with SAT solvers to the Williamson conjecture

Bright, Curtis; Kotsireas, Ilias S.

doi:10.1016/j.jsc.2019.07.024

Cited by 19 publications

(15 citation statements)

References 32 publications

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“…The heuristics used by SLS solvers to solve random SAT problems are also potentially useful for solving real-world SAT problems [47][48][49]. The SAT instances encoded from real-world applications may be of large size.…”

Section: Discussionmentioning

confidence: 99%

“…The propositional satisfiability (SAT) problem is one of the most widely studied NP-complete problems and plays an outstanding role in many domains of computer science and artificial intelligence due to its significant importance in both theory and applications [1]. The SAT problem is fundamental in solving many practical problems in combinatorial optimization, statistical physics, circuit verification, computing theory [2,14], and SAT algorithms have been widely used to solve real-world applications, such as computer algebra systems [9], core computer algebra systems [47], core graphs [48], gene regulatory networks [49], automated verification [54], model-based diagnosis (MBD) [55], scheduling [56], machine induction [57].…”

Section: Introductionmentioning

confidence: 99%

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More efficient stochastic local search for satisfiability

Wu²,

et al. 2020

Appl Intell

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Uniform random satisfiability (URS) and hard random satisfiability (HRS) are two significant generalizations of random satisfiability (RS). Recently, great breakthroughs have been made on stochastic local search (SLS) algorithms for uniform RS, resulting in several state-of-the-art algorithms, e.g., Dimetheus, YalSAT, ProbSAT and Score2SAT. However, compared to the great progress of SLS on URS, the performance of SLS on HRS lags far behind. In this paper, we propose two global clause weighting schemes and a new hybrid scoring function called SA based on a linear combination of a property score and property age, and then apply a second-level-biased random walk strategy based on two clause weighting schemes and SA to develop a new SLS solver called BRSAP. To evaluate the performance of BRSAP, we conduct extensive experiments to compare BRSAP with state-of-the-art SLS solvers and complete solvers on HRS instances and URS instances from SAT Competition 2017 and SAT Competition 2018 as well as 4100 generated satisfiable large HRS and URS ones. The experiments illustrate that BRSAP obviously outperforms its competitors, indicating the effectiveness of BRSAP. We also analyze the effectiveness of the underlying ideas in BRSAP.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

More efficient stochastic local search for satisfiability

Wu²,

et al. 2020

Appl Intell

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“…These searches discovered that Williamson matrices don't exist in the orders n = 35, 47, 53, and 59, but exist in all other orders that were searched. Using MathCheck we were able to provide exhaustive searches for all orders n ≤ 70 divisible by 2 or 3 (finding over 100,000 new sets of Williamson matrices) [13,12] and verified the counterexample n = 35 [10].…”

Section: The Sat+cas Paradigmmentioning

confidence: 99%

The SAT+CAS Method for Combinatorial Search with Applications to Best Matrices

Bright

Djoković

Kotsireas

2019

EasyChair Preprints

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In this paper, we provide an overview of the SAT+CAS method that combines satisfiability checkers (SAT solvers) and computer algebra systems (CAS) to resolve combinatorial conjectures, and present new results vis-à-vis best matrices. The SAT+CAS method is a variant of the Davis-Putnam-Logemann-Loveland DPLL(T ) architecture, where the T solver is replaced by a CAS. We describe how the SAT+CAS method has been previously used to resolve many open problems from graph theory, combinatorial design theory, and number theory, showing that the method has broad applications across a variety of fields. Additionally, we apply the method to construct the largest best matrices yet known and present new skew Hadamard matrices constructed from best matrices. We show the best matrix conjecture (that best matrices exist in all orders of the form r 2 + r + 1) which was previously known to hold for r ≤ 6 also holds for r = 7. We also confirmed the results of the exhaustive searches that have been previously completed for r ≤ 6.

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“…e SAT problem is fundamental in solving many practical problems in combination optimization [3], statistical physics [4], circuit verification [5], and computing theory [6], and SAT algorithms have been widely used to solve real-world applications, such as computer algebra systems [7], core graphs [8], real-time scheduling [9], gene regulatory networks [10], automated verification [11], model-based diagnosis (MBD) [12], and machine induction [13]. erefore, it is of great significance to study SAT problem and improve its solving speed.…”

Section: Introductionmentioning

confidence: 99%

A Topology Graph Algorithm Based on Lattice-Valued Logic to Solve Satisfiability Problems

Tan

2022

Mathematical Problems in Engineering

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Automatic reasoning is a very challenging research area in the field of artificial intelligence. Automatic inference based on lattice-valued logic is an important basic research content in the field of intelligent information processing. It is of great academic significance to deal with incomparability, linguistic valued information, and formal verification of the correctness of corresponding software and hardware systems in various applications. Based on the extensive work of α-resolution automated reasoning in linguistic truth-valued lattice-valued logic, this paper discusses the structure and its α-resolvability of the generalized literal. For further improving the efficiency, a topology graph deduction is proposed as well as its soundness, completeness, and universal algorithm. The use of distributed computing and resource sharing is the core idea of this deduction. In the decision process, as long as one satisfiability solution is found by subtask, the decision result can be given directly, shortening the decision time. The algorithm reduces the time complexity from factorial level to square.

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Applying computer algebra systems with SAT solvers to the Williamson conjecture

Cited by 19 publications

References 32 publications

More efficient stochastic local search for satisfiability

More efficient stochastic local search for satisfiability

The SAT+CAS Method for Combinatorial Search with Applications to Best Matrices

A Topology Graph Algorithm Based on Lattice-Valued Logic to Solve Satisfiability Problems

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