Related papers: Satisfiability Modulo Exponential Integer Arithmet…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
SMT-based program analysis and verification often involve reasoning about program features that have been specified using quantifiers; incorporating quantifiers into SMT-based reasoning is, however, known to be challenging. If quantifier…
Inductive Logic Programming (ILP) provides interpretable rule learning in relational domains, yet remains limited in its ability to induce and reason with numerical constraints. Classical ILP systems operate over discrete predicates and…
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 propose a new quantifier elimination algorithm for the theory of linear real arithmetic. This algorithm uses as subroutine satisfiability modulo this theory, a problem for which there are several implementations available. The quantifier…
Linear programming (LP) is an extremely useful tool and has been successfully applied to solve various problems in a wide range of areas, including operations research, engineering, economics, or even more abstract mathematical areas such…
Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
Quantified formulas pose a significant challenge for Satisfiability Modulo Theories (SMT) solvers due to their inherent undecidability. Existing instantiation techniques, such as e-matching, syntax-guided, model-based, conflict-based, and…
Complexity bounds for many problems on matrices with univariate polynomial entries have been improved in the last few years. Still, for most related algorithms, efficient implementations are not available, which leaves open the question of…
Matrix Riccati differential equations arise in many different areas and are particular important within the field of control theory. In this paper we consider numerical integration for large-scale systems of stiff matrix Riccati…
Program synthesis approaches struggle to learn programs with numerical values. An especially difficult problem is learning continuous values over multiple examples, such as intervals. To overcome this limitation, we introduce an inductive…
Large Language Models (LLMs) are becoming increasingly popular in pervasive computing due to their versatility and strong performance. However, despite their ubiquitous use, the exact mechanisms underlying their outstanding performance…
The optimization of submodular functions on the integer lattice has received much attention recently, but the objective functions of many applications are non-submodular. We provide two approximation algorithms for maximizing a…
Large language models (LLMs) are increasingly relied upon to solve complex mathematical word problems. However, being susceptible to hallucination, they may generate inaccurate results when presented with unanswerable questions, raising…
Polynomial expansions are important in the analysis of neural network nonlinearities. They have been applied thereto addressing well-known difficulties in verification, explainability, and security. Existing approaches span classical Taylor…
We present a novel machine learning architecture that uses the exponential of a single input-dependent matrix as its only nonlinearity. The mathematical simplicity of this architecture allows a detailed analysis of its behaviour, providing…
For a large integer $m,$ we obtain an asymptotic formula for the number of solutions of a certain congruence modulo $m$ with four variables, where the variables belong to special sets of residue classes modulo $m.$ This formula are applied…
Artificial Intelligence problems, ranging form planning/scheduling up to game control, include an essential crucial step: describing a model which accurately defines the problem's required data, requirements, allowed transitions and…