Effective Problem Solving Using SAT Solvers

Bright, Curtis; Gerhard, Jürgen; Kotsireas, Ilias S.

doi:10.1007/978-3-030-41258-6_15

Cited by 13 publications

(11 citation statements)

References 17 publications

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“…It seems that this result on the distribution of propositions has to do with the amazing efficiency of SATsolvers [2,3]. The fact that most of the classical theorems can be solved as "cheap" intuitionistic propositions may explain why SAT-solvers are so efficient and the connection should be further investigated.…”

Section: Discussionmentioning

confidence: 99%

Almost all Classical Theorems are Intuitionistic

Lescanne

2022

RAIRO-Theor. Inf. Appl.

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Canonical expressions represent the implicative propositions (i.e., the propositions with only implications) up-to renaming of variables. Using a Monte-Carlo approach, we explore the model of canonical expressions in order to confirm the paradox that says that asymptotically almost all classical theorems are intuitionistic. Actually we found that more than 96.6% of classical theorems are intuitionistic among propositions of size 100.

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Section: Discussionmentioning

confidence: 99%

Almost all Classical Theorems are Intuitionistic

Lescanne

2022

RAIRO-Theor. Inf. Appl.

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“…We ran benchmarks from the n-Queens problem, using a simple SAT solver based on [17]. In particular, we would like to emphasize that further experiments, as well as systematic comparisons with different parallel tools, will be the subject of future work.…”

Section: Methodsmentioning

confidence: 99%

HermesBDD: A Multi-Core and Multi-Platform Binary Decision Diagram Package

Capogrosso

Geretti

Cristani

et al. 2023

2023 26th International Symposium on Design and Diagnostics of Electronic Circuits and Systems (DDECS)

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BDDs are representations of a Boolean expression in the form of a directed acyclic graph. BDDs are widely used in several fields, particularly in model checking and hardware verification. There are several implementations for BDD manipulation, where each package differs depending on the application. This paper presents HermesBDD: a novel multi-core and multiplatform binary decision diagram package focused on high performance and usability. HermesBDD supports a static and dynamic memory management mechanism, the possibility to exploit lock-free hash tables, and a simple parallel implementation of the IF-THEN-ELSE procedure based on a higher-level wrapper for threads and futures. HermesBDD is completely written in C++ with no need to rely on external libraries and is developed according to software engineering principles for reliability and easy maintenance over time. We provide experimental results on the n-Queens problem, the de-facto SAT solver benchmark for BDDs, demonstrating a significant speedup of 18.73× over our non-parallel baselines, and a remarkable performance boost w.r.t. other state-of-the-art BDDs packages.

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“…In recent years, Boolean satisőability (SAT) solvers have been widely used to solve a variety of combinatorial mathematical problems [10,34]. Given that the minimum KS problem is fundamentally combinatorial in nature, and given that there is a reduction from the KS problem to graph colouringÐan NP-complete problem for which SAT solvers have been shown to be effective [12]Ðit is only natural to consider a reduction from the KS problem to the SAT problem. Such an approach enables a SAT solver to aid in the determination of the cardinality of the minimum-sized KS system.…”

Section: Sat Solvers and Combinatorial Problemsmentioning

confidence: 99%

A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

Bright

2023

Preprint

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One of the most fundamental results in the foundations of quantum mechanics is the Kochen--Specker (KS) theorem, a `no-go' theorem which states that contextuality is an essential feature of any hidden-variable theory. The theorem hinges on the existence of a mathematical object called a KS vector system. Although the existence of a KS vector system was first established by Kochen and Specker, the problem of the minimum size of such a system has stubbornly remained open for over 50 years. In this paper, we present a new method based on a combination of a SAT solver and a computer algebra system (CAS) to address this problem. We improve the lower bound on the minimum number of vectors in a KS system from 22 to 23 and improve the efficiency of the search by a factor of over 1000 when compared to the most recent computational methods. Finding a minimum KS system would simplify experimental tests of the KS theorem and have direct applications in quantum information processing, specifically in the security of quantum cryptographic protocols based on complementarity, zero-error classical communication, and dimension witnessing.

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Effective Problem Solving Using SAT Solvers

Cited by 13 publications

References 17 publications

Almost all Classical Theorems are Intuitionistic

Almost all Classical Theorems are Intuitionistic

HermesBDD: A Multi-Core and Multi-Platform Binary Decision Diagram Package

A SAT Solver + Computer Algebra Attack on the Minimum Kochen-Specker Problem

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