Related papers: Generalized Satisfiability Problems via Operator A…
The model of Dynamic Meta-Constraints has special activity constraints which can activate other constraints. It also has meta-constraints which range over other constraints. An algorithm is presented in which constraints can be assigned one…
The Workflow Satisfiability Problem (WSP) is a problem of practical interest that arises whenever tasks need to be performed by authorized users, subject to constraints defined by business rules. We are required to decide whether there…
We propose a forward-backward splitting dynamical system for solving inclusion problems of the form $0\in A(x)+B(x)$ in Hilbert spaces, where $A$ is a maximal operator and $B$ is a single-valued operator. Involved operators are assumed to…
In this paper, the authors propose a new framework under which a theory of generalized Besov-type and Triebel-Lizorkin-type function spaces is developed. Many function spaces appearing in harmonic analysis fall under the scope of this new…
We study the computational complexity of model checking and satisfiability problems of polyadic modal logics extended with permutations and Boolean operators on accessibility relations. First, we show that the combined complexity of the…
We give the first approximation algorithm for mixed packing and covering semidefinite programs (SDPs) with polylogarithmic dependence on width. Mixed packing and covering SDPs constitute a fundamental algorithmic primitive with recent…
To solve hard problems, AI relies on a variety of disciplines such as logic, probabilistic reasoning, machine learning and mathematical programming. Although it is widely accepted that solving real-world problems requires an integration…
We consider a \emph{family} $(P_\omega)_{\omega \in \Omega}$ of elliptic second order differential operators on a domain $U_0 \subset \mathbb{R}^m$ whose coefficients depend on the space variable $x \in U_0$ and on $\omega \in \Omega,$ a…
In many real world applications of machine learning, models have to meet certain domain-based requirements that can be expressed as constraints (e.g., safety-critical constraints in autonomous driving systems). Such constraints are often…
We intend to create new concepts aimed at finding necessary and sufficient conditions for Boolean satisfiability so that these conditions can be verified in polynomial time. Based on these conditions it will be possible to create an…
In this paper, we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials. We present methods for finding its global minimizers and…
Many AI synthesis problems such as planning or scheduling may be modelized as constraint satisfaction problems (CSP). A CSP is typically defined as the problem of finding any consistent labeling for a fixed set of variables satisfying all…
In this article, we provide a new algorithm for solving constraint satisfaction problems over templates with few subpowers, by reducing the problem to the combination of solvability of a polynomial number of systems of linear equations over…
This paper investigates how global decision problems over arithmetically represented domains acquire reflective structure through class-quantification. Arithmetization forces diagonal fixed points whose verification requires reflection…
The Boolean satisfiability problem (SAT) is of central importance in both theory and practice. Yet, most provable guarantees for quantum algorithms rely exclusively on Grover-type methods that cap the possible advantage at only quadratic…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
We develop a theory of partially defined complete positivity preservers, extending Schoenberg's classical characterization to functions defined only on discrete subsets or constrained domains. We frame the extension problem through the…
This paper summarizes and generalizes a recently proposed mathematical framework that unifies the standard formalisms of special relativity and quantum mechanics. The framework is based on Hilbert spaces H of functions of four space-time…
Representations of Boolean functions by real polynomials play an important role in complexity theory. Typically, one is interested in the least degree of a polynomial p(x_1,...,x_n) that approximates or sign-represents a given Boolean…