相关论文: Local-search techniques for propositional logic ex…
Clause-elimination procedures that simplify formulas in conjunctive normal form play an important role in modern SAT solving. Before or during the actual solving process, such procedures identify and remove clauses that are irrelevant to…
Boolean satisfiability (SAT) solvers are widely used in hardware verification, cryptanalysis, automatic test-pattern generation, and side-channel reasoning workflows. Modern conflict-driven clause-learning (CDCL) solvers are highly…
Cardinality constraints are important in many Sat problems; previous studies provide contradictory conclusions about the best encoding to use. Here, three encodings are compared: Sinz's sequential-counter, Bailleux and Boufkhad's…
In this work, we address the problem of cardinality estimation for similarity search in high-dimensional spaces. Our goal is to design a framework that is lightweight, easy to construct, and capable of providing accurate estimates with…
There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period. Recently quantum computers have surfaced as…
Local Search is one of the fundamental approaches to combinatorial optimization and it is used throughout AI. Several local search algorithms are based on searching the k-exchange neighborhood. This is the set of solutions that can be…
Considering the challenges faced by large language models (LLMs) in logical reasoning and planning, prior efforts have sought to augment LLMs with access to external solvers. While progress has been made on simple reasoning problems,…
A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
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…
In this article, we examine how clausal resolution can be applied to a specific, but widely used, non-classical logic, namely discrete linear temporal logic. Thus, we first define a normal form for temporal formulae and show how arbitrary…
The paper presents a study of local search heuristics in general and variable neighborhood search in particular for the resolution of an assignment problem studied in the practical work of universities. Here, students have to be assigned to…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
Formal verification via theorem proving enables the expressive specification and rigorous proof of software correctness, but it is difficult to scale due to the significant manual effort and expertise required. While Large Language Models…
Goal-directed proof search in first-order logic uses meta-variables to delay the choice of witnesses; substitutions for such variables are produced when closing proof-tree branches, using first-order unification or a theory-specific…
Many reasoning problems are based on the problem of satisfiability (SAT). While SAT itself becomes easy when restricting the structure of the formulas in a certain way, the situation is more opaque for more involved decision problems. We…
Bounded fitting is a general paradigm for learning logical formulas from positive and negative data examples, that has received considerable interest recently. We investigate bounded fitting for the description logic ALC and its syntactic…
ExtractingMUCs(MinimalUnsatisfiableCores)fromanunsatisfiable constraint network is a useful process when causes of unsatisfiability must be understood so that the network can be re-engineered and relaxed to become sat- isfiable. Despite bad…
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…
Large language models (LLMs) have demonstrated remarkable reasoning capabilities across diverse domains. Recent studies have shown that increasing test-time computation enhances LLMs' reasoning capabilities. This typically involves…