Related papers: Necessary and sufficient conditions for Boolean sa…
Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…
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…
We extend the classical notion of solvability to a lambda-calculus equipped with pattern matching. We prove that solvability can be characterized by means of typability and inhabitation in an intersection type system P based on…
Given a set U of alternatives, a choice (correspondence) on U is a contractive map c defined on a family Omega of nonempty subsets of U. Semantically, a choice c associates to each menu A in Omega a nonempty subset c(A) of A comprising all…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…
We explore and relate two notions of monotonicity, stochastic and realizable, for a system of probability measures on a common finite partially ordered set (poset) S when the measures are indexed by another poset A. We give counterexamples…
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.
We propose an approach for decomposing Boolean satisfiability problems while extending recent results of \cite{sul2} on solving Boolean systems of equations. Developments in \cite{sul2} were aimed at the expansion of functions $f$ in…
Conformal Prediction (CP) is a popular method for uncertainty quantification with machine learning models. While conformal prediction provides probabilistic guarantees regarding the coverage of the true label, these guarantees are agnostic…
We identify new sufficiency conditions for coercivity of general multivariate polynomials $f\in\mathbb{R}[x]$ which are expressed in terms of their Newton polytopes at infinity and which consist of a system of affine-linear inequalities in…
Necessary and sufficient conditions are presented for the (first-order) theory of a universal class of algebraic structures (algebras) to admit a model completion, extending a characterization provided by Wheeler. For varieties of algebras…
Understanding properties of deep neural networks is an important challenge in deep learning. In this paper, we take a step in this direction by proposing a rigorous way of verifying properties of a popular class of neural networks,…
Given a classification model and a prediction for some input, there are heuristic strategies for ranking features according to their importance in regard to the prediction. One common approach to this task is rooted in propositional logic…
Constraint Satisfaction Problems (CSP) constitute a convenient way to capture many combinatorial problems. The general CSP is known to be NP-complete, but its complexity depends on a template, usually a set of relations, upon which they are…
The problem of selecting optimal backdoor adjustment sets to estimate causal effects in graphical models with hidden and conditioned variables is addressed. Previous work has defined optimality as achieving the smallest asymptotic…
We consider a variant of the Boolean satisfiability problem where a subset E of the propositional variables appearing in formula Fsat encode a symmetric, transitive, binary relation over N elements. Each of these relational variables,…
Probability of necessity and sufficiency (PNS) measures the likelihood of a feature set being both necessary and sufficient for predicting an outcome. It has proven effective in guiding representation learning for unimodal data, enhancing…
Recent results show that a constraint satisfaction problem (CSP) defined over rational numbers with their natural ordering has a solution if and only if it has a definable solution. The proof uses advanced results from topology and modern…
Boolean satisfiability problems are an important benchmark for questions about complexity, algorithms, heuristics and threshold phenomena. Recent work on heuristics, and the satisfiability threshold has centered around the structure and…