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Boolean satisfiability problem (SAT) is fundamental to many applications. Existing works have used graph neural networks (GNNs) for (approximate) SAT solving. Typical GNN-based end-to-end SAT solvers predict SAT solutions concurrently. We…

Satisfiability checking for Linear Temporal Logic (LTL) is a fundamental step in checking for possible errors in LTL assertions. Extant LTL satisfiability checkers use a variety of different search procedures. With the sole exception of LTL…

The increasing advancements in the field of machine learning have led to the development of numerous applications that effectively address a wide range of problems with accurate predictions. However, in certain cases, accuracy alone may not…

Any satisfiability problem in conjunctive normal form can be solved in polynomial time by reducing it to a 3-sat formulation and transforming this to a Linear Complementarity problem (LCP) which is then solved as a linear program (LP). Any…

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…

We introduce and benchmark a stochastic local search heuristic for the NP-complete satisfiability problem 3-SAT that drastically outperforms existing solvers in the notoriously difficult realm of critically hard instances. Our construction…

Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…

Task arithmetic is a straightforward yet highly effective strategy for model merging, enabling the resultant model to exhibit multi-task capabilities. Recent research indicates that models demonstrating linearity enhance the performance of…

The problem of computing Craig Interpolants has recently received a lot of interest. In this paper, we address the problem of efficient generation of interpolants for some important fragments of first order logic, which are amenable for…

While pre-trained language models achieve impressive performance on various NLP benchmarks, they still struggle with tasks that require numerical reasoning. Recent advances in improving numerical reasoning are mostly achieved using very…

Maximum Satisfiability (MaxSAT) is an optimization variant of the Boolean Satisfiability (SAT) problem. In general, MaxSAT algorithms perform a succession of SAT solver calls to reach an optimum solution making extensive use of cardinality…

We define the concept of a monotonic theory and show how to build efficient SMT (SAT Modulo Theory) solvers, including effective theory propagation and clause learning, for such theories. We present examples showing that monotonic theories…

Training neural networks on NP-complete problems typically demands very large amounts of training data and often needs to be coupled with computationally expensive symbolic verifiers to ensure output correctness. In this paper, we present…

Few-shot prompting and step-by-step reasoning have enhanced the capabilities of Large Language Models (LLMs) in tackling complex tasks including code generation. In this paper, we introduce a prompt selection and augmentation algorithm…

We investigate the domain of satisfiable formulas in satisfiability modulo theories (SMT), in particular, automatic generation of a multitude of satisfying assignments to such formulas. Despite the long and successful history of SMT in…

This paper presents a simple, effective, and cost-efficient strategy to improve LLM performance by scaling test-time compute. Our strategy builds upon the repeated-sampling-then-voting framework, with a novel twist: incorporating multiple…

This paper develops new combinatorial approaches to analyze and compute special set partitions, called complementary set partitions, which are fundamental in the study of generalized cumulants. Moving away from traditional graph-based and…

The past three decades have witnessed notable success in designing efficient SAT solvers, with modern solvers capable of solving industrial benchmarks containing millions of variables in just a few seconds. The success of modern SAT solvers…

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.…

Satisfiability of boolean formulae (SAT) has been a topic of research in logic and computer science for a long time. In this paper we are interested in understanding the structure of satisfiable and unsatisfiable sentences. In previous work…