Related papers: Efficient Encodings of Conditional Cardinality Con…
Optimization problems involving complex variables, when solved, are typically transformed into real variables, often at the expense of convergence rate and interpretability. This paper introduces a novel formalism for a prominent problem in…
I introduce a new family of axioms extending ZFC set theory, the $\Sigma_n$-correct forcing axioms. These assert roughly that whenever a forcing name $\dot{a}$ can be forced by a poset in some forcing class $\Gamma$ to have some $\Sigma_n$…
Contexts are terms with one `hole', i.e. a place in which we can substitute an argument. In context unification we are given an equation over terms with variables representing contexts and ask about the satisfiability of this equation.…
We study local-search satisfiability solvers for propositional logic extended with cardinality atoms, that is, expressions that provide explicit ways to model constraints on cardinalities of sets. Adding cardinality atoms to the language of…
In 2007 it was conjectured that the Constraint Satisfaction Problem (CSP) over a constraint language $\Gamma$ is tractable if and only if $\Gamma$ is preserved by a weak near-unanimity (WNU) operation. After many efforts and partial…
Object counting models suffer when deployed across domains with differing density variety, since density shifts are inherently task-relevant and violate standard domain adaptation assumptions. To address this, we propose a theoretical…
Simple cardinality refers to counting nonzero elements of an independent variable satisfying certain properties. Composite cardinality is a simple counting process composited with an affine mapping, and is therefore more complicated than…
Standard Description Logics (DLs) can encode quantitative aspects of an application domain through either number restrictions, which constrain the number of individuals that are in a certain relationship with an individual, or concrete…
In this paper we investigate some properties of forcing which can be considered "nice" in the context of singularizing regular cardinals to have an uncountable cofinality. We show that such forcing which changes cofinality of a regular…
The minimum number of clauses in a CNF representation of the parity function $x_1 \oplus x_2 \oplus \dotsb \oplus x_n$ is $2^{n-1}$. One can obtain a more compact CNF encoding by using non-deterministic variables (also known as guess or…
We present a unified quantum-classical framework for addressing NP-complete constrained combinatorial optimization problems, generalizing the recently proposed Quantum Conic Programming (QCP) approach. Accordingly, it inherits many…
The well known constant rank constraint qualification [Math. Program. Study 21:110--126, 1984] introduced by Janin for nonlinear programming has been recently extended to a conic context by exploiting the eigenvector structure of the…
Functional constraints and bi-functional constraints are an important constraint class in Constraint Programming (CP) systems, in particular for Constraint Logic Programming (CLP) systems. CP systems with finite domain constraints usually…
Modern language models represent probability distributions over character strings as distributions over (shorter) token strings derived via a deterministic tokenizer, such as byte-pair encoding. While this approach is highly effective at…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…
This paper explores the computational complexity of various natural one-variable fragments of first-order modal logics with the addition of counting quantifiers, over both constant and varying domains. The addition of counting quantifiers…
In the paper a new sufficient condition for the Aubin property to a class of parameterized variational systems is derived. In these systems the constraints depend both on the parameter as well as on the decision variable itself and they…
Spectral clustering is popular among practitioners and theoreticians alike. While performance guarantees for spectral clustering are well understood, recent studies have focused on enforcing ``fairness'' in clusters, requiring them to be…
High\-cardinality categorical variables pose significant challenges in machine learning, particularly in terms of computational efficiency and model interpretability. Traditional one\-hot encoding often results in high\-dimensional sparse…