Related papers: SAT-based Analysis of Large Real-world Feature Mod…

Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive…

Earlier we introduced the notion of a stable set of points (SSP). We proved that a CNF formula is unsatisfiable iff there is a set of points (i.e. complete assignments) that is stable with respect to this formula. Experiments showed that…

Over the past few decades, combinatorial solvers have seen remarkable performance improvements, enabling their practical use in real-world applications. In some of these applications, ensuring the correctness of the solver's output is…

In this work, we present a novel technique for GPU-accelerated Boolean satisfiability (SAT) sampling. Unlike conventional sampling algorithms that directly operate on conjunctive normal form (CNF), our method transforms the logical…

Propositional satisfiability (SAT) solvers, which typically operate using conjunctive normal form (CNF), have been successfully applied in many domains. However, in some application areas such as circuit verification, bounded model…

We study $q$-SAT in the multistage model, focusing on the linear-time solvable 2-SAT. Herein, given a sequence of $q$-CNF fomulas and a non-negative integer $d$, the question is whether there is a sequence of satisfying truth assignments…

Fine-tuning Large Language Models (LLMs) has emerged as a common practice for tailoring models to individual needs and preferences. The choice of datasets for fine-tuning can be diverse, introducing safety concerns regarding the potential…

Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…

Satisfiability modulo nonlinear real arithmetic theory (SMT(NRA)) solving is essential to multiple applications, including program verification, program synthesis and software testing. In this context, recently model constructing…

This paper describes a novel unbounded software model checking approach to find errors in programs written in the C language based on incremental SAT-solving. Instead of using the traditional assumption based API to incremental SAT solvers…

Recent advances in Large Language Models (LLMs) have demonstrated remarkable general reasoning capabilities. However, systematically evaluating and enhancing these reasoning capabilities is challenging due to the lack of controllable and…

This paper gives a novel approach to analyze SAT problem more deeply. First, I define new elements of Boolean formula such as dominant variable, decision chain, and chain coupler. Through the analysis of the SAT problem using the elements,…

Large language models (LLMs) have opened new paradigms in optimization modeling by enabling the generation of executable solver code from natural language descriptions. Despite this promise, existing approaches typically remain…

Constrained Horn Clauses (CHCs) are often used in automated program verification. Thus, techniques for (dis-)proving satisfiability of CHCs are a very active field of research. On the other hand, acceleration techniques for computing…

This paper introduces a new approach to solving a continuous-time version of the multi-agent path finding problem. The algorithm translates the problem into an extension of the classical Boolean satisfiability problem, satisfiability modulo…

Generations from large language models (LLMs) can be improved by sampling and scoring multiple solutions to select a final answer. Current "sample and select" methods such as self-consistency (SC) rely on majority voting to score answers.…

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…

In this paper, we propose a constraint-based modeling approach for the problem of discovering frequent gradual patterns in a numerical dataset. This SAT-based declarative approach offers an additional possibility to benefit from the recent…

Large Language Models (LLMs) prompted to generate chain-of-thought (CoT) exhibit impressive reasoning capabilities. Recent attempts at prompt decomposition toward solving complex, multi-step reasoning problems depend on the ability of the…

We propose a new approach to SAT solving which solves SAT problems in vector spaces as a cost minimization problem of a non-negative differentiable cost function J^sat. In our approach, a solution, i.e., satisfying assignment, for a SAT…