Related papers: Pushing the envelope of Optimization Modulo Theori…
In the contexts of automated reasoning (AR) and formal verification (FV), important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for…
In the contexts of automated reasoning and formal verification, important decision problems are effectively encoded into Satisfiability Modulo Theories (SMT). In the last decade efficient SMT solvers have been developed for several theories…
Optimization Modulo Theories (OMT) has emerged as an important extension of the highly successful Satisfiability Modulo Theories (SMT) paradigm. The OMT problem requires solving an SMT problem with the restriction that the solution must be…
Optimization Modulo Theories (OMT) is an extension of SMT that allows for finding models that optimize objective functions. In this paper we aim at bridging the gap between Constraint Programming (CP) and OMT, in both directions. First, we…
Optimization Modulo Theories (OMT) is an extension of SMT which allows for finding models that optimize given objectives. (Partial weighted) MaxSMT --or equivalently OMT with Pseudo-Boolean objective functions, OMT+PB-- is a very-relevant…
Optimization Modulo Theories (OMT) is an important extension of SMT which allows for finding models that optimize given objective functions, typically consisting in linear-arithmetic or pseudo-Boolean terms. However, many SMT and OMT…
Optimization Modulo Theories (OMT) extends Satisfiability Modulo Theories (SMT) with the task of optimizing some objective function(s). In OMT solvers, a CDCL-based SMT solver enumerates theory-satisfiable total truth assignments, and a…
Satisfiability Modulo Theory (SMT) has recently emerged as a powerful tool for solving various automated reasoning problems across diverse domains. Unlike traditional satisfiability methods confined to Boolean variables, SMT can reason on…
In manufacturing, the increasing involvement of autonomous robots in production processes poses new challenges on the production management. In this paper we report on the usage of Optimization Modulo Theories (OMT) to solve certain…
SMT solvers use sophisticated techniques for polynomial (linear or non-linear) integer arithmetic. In contrast, non-polynomial integer arithmetic has mostly been neglected so far. However, in the context of program verification, polynomials…
We establish numerical methods for solving the martingale optimal transport problem (MOT) - a version of the classical optimal transport with an additional martingale constraint on transport's dynamics. We prove that the MOT value can be…
We investigate the capabilities and scalability of Large Language Models (LLMs) in optimization modeling, a domain requiring structured reasoning and precise formulation. To this end, we introduce OPT-ENGINE, an extensible benchmark…
The problem of finding small unsatisfiable cores for SAT formulas has recently received a lot of interest, mostly for its applications in formal verification. However, propositional logic is often not expressive enough for representing many…
#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…
We present new methods for solving the Satisfiability Modulo Theories problem over the theory of Quantifier-Free Non-linear Integer Arithmetic, SMT(QF-NIA), which consists in deciding the satisfiability of ground formulas with integer…
Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…
The Circuit Satisfiability (CSAT) problem, a variant of the Boolean Satisfiability (SAT) problem, plays a critical role in integrated circuit design and verification. However, existing SAT solvers, optimized for Conjunctive Normal Form…
The ability to generate test data is often a necessary prerequisite for automated software testing. For the generated data to be fit for its intended purpose, the data usually has to satisfy various logical constraints. When testing is…
Satisfiability modulo theory (SMT) consists in testing the satisfiability of first-order formulas over linear integer or real arithmetic, or other theories. In this survey, we explain the combination of propositional satisfiability and…
Large language models (LLMs) are displaying emergent abilities for math reasoning tasks,and there is a growing attention on enhancing the ability of open-source LLMs through supervised fine-tuning (SFT).In this paper, we aim to explore a…