Related papers: Computing Small Unsatisfiable Cores in Satisfiabil…

Symmetry breaking is a popular technique to reduce the search space for SAT solving by exploiting the underlying symmetry over variables and clauses in a formula. The key idea is to first identify sets of assignments which fall in the same…

In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.

Chain-of-Thought (CoT) prompting enhances the reasoning of large language models (LLMs) by decomposing problems into sequential steps, mimicking human logic and reducing errors. However, complex tasks with vast solution spaces and vague…

We present Integer Linear Programming (ILP) Modulo Theories (IMT). An IMT instance is an Integer Linear Programming instance, where some symbols have interpretations in background theories. In previous work, the IMT approach has been…

Efficiently determining the satisfiability of a boolean equation -- known as the SAT problem for brevity -- is crucial in various industrial problems. Recently, the advent of deep learning methods has introduced significant potential for…

Universal quantifiers occur frequently in proof obligations produced by program verifiers, for instance, to axiomatize uninterpreted functions and to express properties of arrays. SMT-based verifiers typically reason about them via…

Despite demonstrating emergent reasoning abilities, Large Language Models (LLMS) often lose track of complex, multi-step reasoning. Existing studies show that providing guidance via decomposing the original question into multiple…

Large Language Models (LLMs) are often used as automated judges to evaluate text, but their effectiveness can be hindered by various unintentional biases. We propose using linear classifying probes, trained by leveraging differences between…

Large Language Models (LLMs) are frequently used for multi-faceted language generation and evaluation tasks that involve satisfying intricate user constraints or taking into account multiple aspects and criteria. However, their performance…

The evaluation of mathematical reasoning capabilities is essential for advancing Artificial General Intelligence (AGI). While Large Language Models (LLMs) have shown impressive performance in solving mathematical problems, existing…

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…

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and…

We present a novel approach for solving quantified bit-vector formulas in Satisfiability Modulo Theories (SMT) based on computing symbolic inverses of bit-vector operators. We derive conditions that precisely characterize when bit-vector…

The theory of uninterpreted functions is a key modeling tool for systems with unknown or abstracted components. Some domains such as systems biology impose further restrictions regarding monotonicity on these components, requiring specific…

Large language models (LLMs) demonstrate impressive capabilities in mathematical reasoning. However, despite these achievements, current evaluations are mostly limited to specific mathematical topics, and it remains unclear whether LLMs are…

Due to the size and complexity of modern large language models (LLMs), it has proven challenging to uncover the underlying mechanisms that models use to solve reasoning problems. For instance, is their reasoning for a specific problem…

Small language models (SLMs) offer computational efficiency for scalable deployment, yet they often fall short of the reasoning power exhibited by their larger counterparts (LLMs). To mitigate this gap, current approaches invoke an LLM to…

Solving constraints involving inductive (aka recursive) definitions is challenging. State-of-the-art SMT/CHC solvers and first-order logic provers provide only limited support for solving such constraints, especially when they involve,…

The CTL learning problem consists in finding for a given sample of positive and negative Kripke structures a distinguishing CTL formula that is verified by the former but not by the latter. Further constraints may bound the size and shape…

We study the complexity of reasoning tasks for logics in team semantics. Our main focus is on the data complexity of model checking but we also derive new results for logically defined counting and enumeration problems. Our approach is…