Related papers: More is Less: Adding Polynomials for Faster Explan…
Scaling test-time compute brings substantial performance gains for large language models (LLMs). By sampling multiple answers and heuristically aggregate their answers (e.g., either through majority voting or using verifiers to rank the…
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…
The Maximum Satisfiability (MaxSAT) problem is the problem of finding a truth assignment that maximizes the number of satisfied clauses of a given Boolean formula in Conjunctive Normal Form (CNF). Many exact solvers for MaxSAT have been…
This paper describes diff-SAT, an Answer Set and SAT solver which combines regular solving with the capability to use probabilistic clauses, facts and rules, and to sample an optimal world-view (multiset of satisfying Boolean variable…
The computational complexity of solving random 3-Satisfiability (3-SAT) problems is investigated. 3-SAT is a representative example of hard computational tasks; it consists in knowing whether a set of alpha N randomly drawn logical…
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…
Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive…
In this paper, we present a new, graph-based modeling approach and a polynomial-sized linear programming (LP) formulation of the Boolean satisfiability problem (SAT). The approach is illustrated with a numerical example.
A novel parallel algorithm for solving the classical Decision Boolean Satisfiability problem with clauses in conjunctive normal form is depicted. My approach for solving SAT is without using algebra or other computational search strategies…
LLMs face significant challenges in systematic generalization, particularly when dealing with reasoning tasks requiring compositional rules and handling out-of-distribution examples. To address these challenges, we introduce an in-context…
We present a method for the synthesis of polynomial lasso programs. These programs consist of a program stem, a set of transitions, and an exit condition, all in the form of algebraic assertions (conjunctions of polynomial equalities).…
MaxSAT, the optimization version of the well-known SAT problem, has attracted a lot of research interest in the last decade. Motivated by the many important applications and inspired by the success of modern SAT solvers, researchers have…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
Recent formal approaches towards causality have made the concept ready for incorporation into the technical world. However, causality reasoning is computationally hard; and no general algorithmic approach exists that efficiently infers the…
We give a first account of our new parallel SAT solver Gimsatul. Its key feature is to share clauses physically in memory instead of copying them, which is the method of other state-of-the-art multi-threaded SAT solvers to exchange clauses…
We propose an incomplete algorithm for Maximum Satisfiability (MaxSAT) specifically designed to run on neural network accelerators such as GPUs and TPUs. Given a MaxSAT problem instance in conjunctive normal form, our procedure constructs a…
The 3-Satisfiability Problem (3-SAT) is a demanding combinatorial problem, of central importance among the non-deterministic polynomial (NP) complete problems, with applications in circuit design, artificial intelligence and logistics. Even…
The ability to learn polynomials and generalize out-of-distribution is essential for simulation metamodels in many disciplines of engineering, where the time step updates are described by polynomials. While feed forward neural networks can…
In this work, we study how to use sampling to speed up mechanisms for answering adaptive queries into datasets without reducing the accuracy of those mechanisms. This is important to do when both the datasets and the number of queries asked…
By creating some new concepts and methods: checking tree, long unit path, direct contradiction unit pair, indirect contradiction unit pair, additional contradiction unit pair, 2-unit layer and 3-unit layer, redundant units, and destroying…