Related papers: Satisfiability Modulo Exponential Integer Arithmet…
Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has…
Satisfiability-based verification techniques, leveraging modern Boolean satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers, have demonstrated efficacy in addressing practical problem instances within program analysis.…
Despite the remarkable success of Transformer-based large language models (LLMs) across various domains, understanding and enhancing their mathematical capabilities remains a significant challenge. In this paper, we conduct a rigorous…
Boolean Satisfiability (SAT) problems are expressed as mathematical formulas. This paper presents a matrix representation for these SAT problems. It shows how to use this matrix representation to get the full set of valid satisfying…
Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems. However, like standard solvers, they suffer performance penalties for certain stiff systems,…
Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is…
Feature attribution methods are popular for explaining neural network predictions, and they are often evaluated on metrics such as comprehensiveness and sufficiency. In this paper, we highlight an intriguing property of these metrics: their…
For typical first-order logical theories, satisfying assignments have a straightforward finite representation that can directly serve as a certificate that a given assignment satisfies the given formula. For non-linear real arithmetic…
In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…
Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…
Using Maple, we implement a SAT solver based on the principle of inclusion-exclusion and the Bonferroni inequalities. Using randomly generated input, we investigate the performance of our solver as a function of the number of variables and…
We present a novel approach for solving quantified bit-vector formulas in Satisfiability Modulo Theories (SMT) based on computing symbolic inverses of bit-vector operators. We derive conditions that precisely characterize when bit-vector…
We apply Boolean Satisfiability (SAT) and Satisfiability Modulo Theories (SMT) solvers in the context of finding chiral heterotic string models with positive cosmological constant from $\mathbb{Z}_2\times \mathbb{Z}_2$ orbifolds. The power…
Constraint answer set programming integrates answer set programming with constraint processing. System EZSMT+ is a constraint answer set programming tool that utilizes satisfiability modulo theory solvers for search. Its theoretical…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
This paper introduces the exponential substitution calculus (ESC), a new presentation of cut elimination for IMELL, based on proof terms and building on the idea that exponentials can be seen as explicit substitutions. The idea in itself is…
This paper deals with the algorithmic aspects of solving feasibility problems of semidefinite programming (SDP), aka linear matrix inequalities (LMI). Since in some SDP instances all feasible solutions have irrational entries, numerical…
Recent techniques that integrate \emph{solver layers} into Deep Neural Networks (DNNs) have shown promise in bridging a long-standing gap between inductive learning and symbolic reasoning techniques. In this paper we present a set of…
Numerical solutions of differential equations are usually not smooth functions. However, they should resemble the smoothness of the corresponding real solutions in one way or another. In two of our recent papers, a kind of spacial…
We improve and refine a method for certifying that the values' sizes computed by an imperative program will be bounded by polynomials in the program's inputs' sizes. Our work ''tames'' the non-determinism of the original analysis, and…