Related papers: Self-Satisfied: An end-to-end framework for SAT ge…
Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…
The aim of this short note is mainly pedagogical. It summarizes some knowledge about Boolean satisfiability (SAT) and the P=NP? problem in an elementary mathematical language. A convenient scheme to visualize and manipulate CNF formulae is…
This paper explores the Boolean Satisfiability Problem (SAT) in the context of Kolmogorov complexity theory. We present three versions of the distinguishability problem-Boolean formulas, Turing machines, and quantum systems-each focused on…
Using methods and ideas from statistical mechanics, we propose a simple method for obtaining rigorous upper bounds for satisfiability transition in random boolean expressions composed of N variables and M clauses with K variables per…
Boolean satisfiability (SAT) solving is a fundamental problem in computer science. Finding efficient algorithms for SAT solving has broad implications in many areas of computer science and beyond. Quantum SAT solvers have been proposed in…
A major problem in evaluating stochastic local search algorithms for NP-complete problems is the need for a systematic generation of hard test instances having previously known properties of the optimal solutions. On the basis of…
We develop a hypergraph container method for the Boolean Satisfiability Problem (SAT) via the newly developed container results [Campos and Samotij (2024)]. This provides an explicit connection between the extent of spread of clauses and…
When solving a combinatorial problem using propositional satisfiability (SAT), the encoding of the problem is of vital importance. We study encodings of Pseudo-Boolean (PB) constraints, a common type of arithmetic constraint that appears in…
Foundational optimization embeddings have recently emerged as powerful pre-trained representations for mixed-integer programming (MIP) problems. These embeddings were shown to enable cross-domain transfer and reduce reliance on…
Feature extraction is a fundamental task in the application of machine learning methods to SAT solving. It is used in algorithm selection and configuration for solver portfolios and satisfiability classification. Many approaches have been…
Many difficult computational problems involve the simultaneous satisfaction of multiple constraints which are individually easy to satisfy. Such problems occur in diffractive imaging, protein folding, constrained optimization (e.g., spin…
Satisfiability-based automated reasoning is an approach that is being successfully used in software engineering to validate complex software, including for safety-critical systems. Such reasoning underlies many validation activities, from…
We investigate the domain of satisfiable formulas in satisfiability modulo theories (SMT), in particular, automatic generation of a multitude of satisfying assignments to such formulas. Despite the long and successful history of SMT in…
We apply Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers in the context of finding chiral heterotic string models with positive cosmological constant from $\mathbb{Z}_2\times \mathbb{Z}_2$ orbifolds. The power…
We model Semantic Self-Verification (SSV) as the problem of determining whether a statement accurately characterizes its own semantic properties within a given interpretive framework that formalizes a challenge in AI safety and fairness:…
We study preprocessing techniques for clause normal forms of LTL formulas. Applying the mechanism of labelled clauses enables us to reinterpret LTL satisfiability as a set of purely propositional problems and thus to transfer simplification…
We propose Differentiable Satisfiability and Differentiable Answer Set Programming (Differentiable SAT/ASP) for multi-model optimization. Models (answer sets or satisfying truth assignments) are sampled using a novel SAT/ASP solving…
Boolean satisfiability (SAT) is a propositional logic problem of determining whether an assignment of variables satisfies a Boolean formula. Many combinatorial optimization problems can be formulated in Boolean SAT logic -- either as k-SAT…
We present an executable formally verified SAT encoding of classical AI planning. We use the theorem prover Isabelle/HOL to perform the verification. We experimentally test the verified encoding and show that it can be used for reasonably…
Constrained sampling and counting are two fundamental problems in artificial intelligence with a diverse range of applications, spanning probabilistic reasoning and planning to constrained-random verification. While the theory of these…