177 research outputs found
A Time Leap Challenge for SAT Solving
We compare the impact of hardware advancement and algorithm advancement for
SAT solving over the last two decades. In particular, we compare 20-year-old
SAT-solvers on new computer hardware with modern SAT-solvers on 20-year-old
hardware. Our findings show that the progress on the algorithmic side has at
least as much impact as the progress on the hardware side.Comment: Authors' version of a paper which is to appear in the proceedings of
CP'202
Encodings of problems in effectively propositional logic
Solving various combinatorial problems by their translation to the propositional satisfiability problem has become commonly accepted. By optimising such translations and using efficient SAT solvers one can often solve hard problems in various domains, such as formal verification and planning
New Boolean satisfiability problem heuristic strategy: Minimal Positive Negative Product Strategy
This study presents a novel heuristic algorithm called the "Minimal Positive
Negative Product Strategy" to guide the CDCL algorithm in solving the Boolean
satisfiability problem. It provides a mathematical explanation for the
superiority of this algorithm over widely used heuristics such as the Dynamic
Largest Individual Sum (DLIS) and the Variable State Independent Decaying Sum
(VSIDS). Experimental results further confirm the effectiveness of this
heuristic strategy in problem-solving.Comment: 7 pages, 2 figure
A novel EGs-based framework for systematic propositional-formula simplification
Funding: Bowles is partially supported by Austrian FWF Meitner Fellowship M-3338 N.This paper presents a novel simplification calculus for propositional logic derived from Peirce’s Existential Graphs’ rules of inference and implication graphs. Our rules can be applied to arbitrary propositional logic formulae (not only in CNF), are equivalence-preserving, guarantee a monotonically decreasing number of clauses and literals, and maximise the preservation of structural problem information. Our techniques can also be seen as higher-level SAT preprocessing, and we show how one of our rules (TWSR) generalises and streamlines most of the known equivalence-preserving SAT preprocessing methods. We further show how this rule can be extended with a novel n-ary implication graph to capture all known equivalence-preserving preprocessing procedures. Finally, we discuss the complexity and implementation of our framework as a solver-agnostic algorithm to simplify Boolean satisfiability problems and arbitrary propositional formula.Postprin
SAT Competition 2020
The SAT Competitions constitute a well-established series of yearly open international algorithm implementation competitions, focusing on the Boolean satisfiability (or propositional satisfiability, SAT) problem. In this article, we provide a detailed account on the 2020 instantiation of the SAT Competition, including the new competition tracks and benchmark selection procedures, overview of solving strategies implemented in top-performing solvers, and a detailed analysis of the empirical data obtained from running the competition
SAT Competition 2020
The SAT Competitions constitute a well-established series of yearly open international algorithm implementation competitions, focusing on the Boolean satisfiability (or propositional satisfiability, SAT) problem. In this article, we provide a detailed account on the 2020 instantiation of the SAT Competition, including the new competition tracks and benchmark selection procedures, overview of solving strategies implemented in top-performing solvers, and a detailed analysis of the empirical data obtained from running the competition. (C) 2021 The Authors. Published by Elsevier B.V.Peer reviewe
Unveiling the Limits of Learned Local Search Heuristics: Are You the Mightiest of the Meek?
In recent years, combining neural networks with local search heuristics has
become popular in the field of combinatorial optimization. Despite its
considerable computational demands, this approach has exhibited promising
outcomes with minimal manual engineering. However, we have identified three
critical limitations in the empirical evaluation of these integration attempts.
Firstly, instances with moderate complexity and weak baselines pose a challenge
in accurately evaluating the effectiveness of learning-based approaches.
Secondly, the absence of an ablation study makes it difficult to quantify and
attribute improvements accurately to the deep learning architecture. Lastly,
the generalization of learned heuristics across diverse distributions remains
underexplored. In this study, we conduct a comprehensive investigation into
these identified limitations. Surprisingly, we demonstrate that a simple
learned heuristic based on Tabu Search surpasses state-of-the-art (SOTA)
learned heuristics in terms of performance and generalizability. Our findings
challenge prevailing assumptions and open up exciting avenues for future
research and innovation in combinatorial optimization
Recognition and Exploitation of Gate Structure in SAT Solving
In der theoretischen Informatik ist das SAT-Problem der archetypische Vertreter der Klasse der NP-vollständigen Probleme, weshalb effizientes SAT-Solving im Allgemeinen als unmöglich angesehen wird.
Dennoch erzielt man in der Praxis oft erstaunliche Resultate, wo einige Anwendungen Probleme mit Millionen von Variablen erzeugen, die von neueren SAT-Solvern in angemessener Zeit gelöst werden können.
Der Erfolg von SAT-Solving in der Praxis ist auf aktuelle Implementierungen des Conflict Driven Clause-Learning (CDCL) Algorithmus zurückzuführen, dessen Leistungsfähigkeit weitgehend von den verwendeten Heuristiken abhängt, welche implizit die Struktur der in der industriellen Praxis erzeugten Instanzen ausnutzen.
In dieser Arbeit stellen wir einen neuen generischen Algorithmus zur effizienten Erkennung der Gate-Struktur in CNF-Encodings von SAT Instanzen vor, und außerdem drei Ansätze, in denen wir diese Struktur explizit ausnutzen.
Unsere Beiträge umfassen auch die Implementierung dieser Ansätze in unserem SAT-Solver Candy und die Entwicklung eines Werkzeugs für die verteilte Verwaltung von Benchmark-Instanzen und deren Attribute, der Global Benchmark Database (GBD)
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