Related papers: Optimization Modulo Theories with Linear Rational …

In the last two decades, modal and description logics have been applied to numerous areas of computer science, including knowledge representation, formal verification, database theory, distributed computing and, more recently, semantic web…

We consider the problem of solving floating-point constraints obtained from software verification. We present UppSAT --- a new implementation of a systematic approximation refinement framework [ZWR17] as an abstract SMT solver. Provided…

We introduce an approach that aims to combine the usage of satisfiability modulo theories (SMT) solvers with the Combinatory Logic Synthesizer (CL)S framework. (CL)S is a tool for the automatic composition of software components from a…

The remarkable achievements of machine learning techniques in analyzing discrete structures have drawn significant attention towards their integration into combinatorial optimization algorithms. Typically, these methodologies improve…

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…

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 consider the problem of globally minimizing the sum of many rational functions over a given compact semialgebraic set. The number of terms can be large (10 to 100), the degree of each term should be small (up to 10), and the number of…

Recent research in areas such as SAT solving and Integer Linear Programming has shown that the performances of a single arbitrarily efficient solver can be significantly outperformed by a portfolio of possibly slower on-average solvers. We…

The work we describe here is a part of a research program of developing foundations of declarative solving of search problems. We consider the model expansion task as the task representing the essence of search problems where we are given…

Optimization of Mixed-Integer Non-Linear Programming (MINLP) supports important decisions in applications such as Chemical Process Engineering. But current solvers have limited ability for deductive reasoning or the use of domain-specific…

This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…

Modern software for propositional satisfiability problems gives a powerful automated reasoning toolkit, capable of outputting not only a satisfiable/unsatisfiable signal but also a justification of unsatisfiability in the form of resolution…

We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…

Generative large language models (LLMs) with instruct training such as GPT-4 can follow human-provided instruction prompts and generate human-like responses to these prompts. Apart from natural language responses, they have also been found…

In many applications, SMT solvers are utilized to solve similar or identical tasks over time. Significant variations in performance due to small changes in the input are not uncommon and lead to frustration for users. This sort of stability…

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 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…

We present here a new explicit reasoning framework for linear temporal logic (LTL), which is built on top of propositional satisfiability (SAT) solving. As a proof-of-concept of this framework, we describe a new LTL satisfiability tool,…

The problem of computing Craig interpolants in SAT and SMT has recently received a lot of interest, mainly for its applications in formal verification. Efficient algorithms for interpolant generation have been presented for some theories of…

Large language models (LLMs) have shown limitations in tasks requiring complex logical reasoning and multi-step problem-solving. To address these challenges, researchers have employed carefully designed prompts and flowcharts, simulating…