Related papers: Optimization Modulo Theories with Linear Rational …
Local search has recently been applied to SMT problems over various arithmetic theories. Among these, nonlinear real arithmetic poses special challenges due to its uncountable solution space and potential need to solve higher-degree…
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…
We develop a simple functional programming language aimed at manipulating infinite, but first-order definable structures, such as the countably infinite clique graph or the set of all intervals with rational endpoints. Internally, such sets…
We discuss the topic of unsatisfiability proofs in SMT, particularly with reference to quantifier free non-linear real arithmetic. We outline how the methods here do not admit trivial proofs and how past formalisation attempts are not…
Maximum Satisfiability (MaxSAT) is a well-known optimization pro- blem, with several practical applications. The most widely known MAXS AT algorithms are ineffective at solving hard problems instances from practical application domains.…
Machine learning is a thriving part of computer science. There are many efficient approaches to machine learning that do not provide strong theoretical guarantees, and a beautiful general learning theory. Unfortunately, machine learning…
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…
Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI.…
This paper investigates the capabilities of large language models (LLMs) in formulating and solving decision-making problems using mathematical programming. We first conduct a systematic review and meta-analysis of recent literature to…
Goal models have been widely used in Computer Science to represent software requirements, business objectives, and design qualities. Existing goal modelling techniques, however, have shown limitations of expressiveness and/or tractability…
Reasoning about array data structures is a key requirement for many applications in hardware and software verification, especially in combination with machine integers. The Satisfiability Modulo Theories (SMT) theory of extensional arrays…
All-Solution Satisfiability (AllSAT) and its extension, All-Solution Satisfiability Modulo Theories (AllSMT), have become more relevant in recent years, mainly in formal verification and artificial intelligence applications. The goal of…
Satisfiability Modulo Theories (SMT) solvers check the satisfiability of quantifier-free first-order logic formulas. We consider the theory of non-linear real arithmetic where the formulae are logical combinations of polynomial constraints.…
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…
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…
Large language models (LLMs) are increasingly used for tasks that implicitly reduce to Boolean satisfiability (SAT), yet their reasoning ability on SAT remains unclear. We present a systematic study of LLMs on 2-SAT and 3-SAT, together with…
We use SMT technology to address a class of problems involving uninterpreted functions and nonlinear real arithmetic. In particular, we focus on problems commonly found in mathematical competitions, such as the International Mathematical…
Mathematical optimization is ubiquitous in modern applications. However, in practice, we often need to use nonlinear optimization models, for which the existing optimization tools such as Cplex or Gurobi may not be directly applicable and…
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…
Software Pipelining is a classic and important loop-optimization for VLIW processors. It improves instruction-level parallelism by overlapping multiple iterations of a loop and executing them in parallel. Typically, it is implemented using…