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The Boolean Satisfiability problem (SAT), as the prototypical $\mathsf{NP}$-complete problem, is crucial in both theoretical computer science and practical applications. To address this problem, stochastic local search (SLS) algorithms,…
Large Reasoning Models (LRMs) have revolutionized complex problem-solving, yet they exhibit a pervasive "overthinking", generating unnecessarily long reasoning chains. While current solutions improve token efficiency, they often sacrifice…
#SMT, or model counting for logical theories, is a well-known hard problem that generalizes such tasks as counting the number of satisfying assignments to a Boolean formula and computing the volume of a polytope. In the realm of…
Many experts argue that the future of artificial intelligence is limited by the field's ability to integrate symbolic logical reasoning into deep learning architectures. The recently proposed differentiable MAXSAT solver, SATNet, was a…
Satisfiability Modulo Theories (SMT) solvers incorporate decision procedures for theories of data types that commonly occur in software. This makes them important tools for automating verification problems. A limitation frequently…
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…
To solve Math Word Problems, human students leverage diverse reasoning logic that reaches different possible equation solutions. However, the mainstream sequence-to-sequence approach of automatic solvers aims to decode a fixed solution…
Current implementations of pseudo-Boolean (PB) solvers working on native PB constraints are based on the CDCL architecture which empowers highly efficient modern SAT solvers. In particular, such PB solvers not only implement a…
Large language models (LLMs) are capable of solving a wide range of tasks, yet they have struggled with reasoning. To address this, we propose $\textbf{Additional Logic Training (ALT)}$, which aims to enhance LLMs' reasoning capabilities by…
Z3-Noodler is a fork of Z3 that replaces its string theory solver with a custom solver implementing the recently introduced stabilization-based algorithm for solving word equations with regular constraints. An extensive experimental…
Mathematical reasoning remains a challenging area for large language models (LLMs), prompting the development of math-specific LLMs such as LLEMMA, DeepSeekMath, and Qwen2-Math, among others. These models typically follow a two-stage…
We build a SAT solver implementing the DPLL algorithm in the verification-enabled programming language Dafny. The resulting solver is fully verified (soundness, completeness and termination are computer checked). We benchmark our Dafny…
Concurrent systems are notoriously difficult to analyze, and technological advances such as weak memory architectures greatly compound this problem. This has renewed interest in partial order semantics as a theoretical foundation for formal…
Nowadays, Large Language Models (LLMs) have been gradually employed to solve complex tasks. To face the challenge, task decomposition has become an effective way, which proposes to divide a complex task into multiple simpler subtasks and…
Propositional bounded model checking has been applied successfully to verify embedded software but is limited by the increasing propositional formula size and the loss of structure during the translation. These limitations can be reduced by…
We give an overview of recent techniques for implementing syntax-guided synthesis (SyGuS) algorithms in the core of Satisfiability Modulo Theories (SMT) solvers. We define several classes of synthesis conjectures and corresponding…
Satisfiability modulo theories (SMT) solvers have throughout the years been able to cope with increasingly expressive formulas, from ground logics to full first-order logic modulo theories. Nevertheless, higher-order logic within SMT is…
In this work, we provide a systematic analysis of how large language models (LLMs) contribute to solving planning problems. In particular, we examine how LLMs perform when they are used as problem solver, solution verifier, and heuristic…
Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops…
We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that…