Related papers: Unsatisfiable CNF Formulas need many Conflicts
The theory of belief functions is an effective tool to deal with the multiple uncertain information. In recent years, many evidence combination rules have been proposed in this framework, such as the conjunctive rule, the cautious rule, the…
The condition number of solutions to full rank linear least-squares problem are shown to be given by an optimization problem that involves nuclear norms of rank 2 matrices. The condition number is with respect to the least-squares…
We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_*(k)$ such that a random $k$-SAT formula of clause density $\alpha$ is with…
Answer set programs used in real-world applications often require that the program is usable with different input data. This, however, can often lead to contradictory statements and consequently to an inconsistent program. Causes for…
We consider the random regular $k$-NAE-SAT problem with $n$ variables each appearing in exactly $d$ clauses. For all $k$ exceeding an absolute constant $k_0$, we establish explicitly the satisfiability threshold $d_*=d_*(k)$. We prove that…
Inspired by the work of Newhouse in one real variable, we introduce a relevant notion of thickness for dynamical Cantor sets of the plane associated to a holomorphic IFS. Our main result is a complex version of Newhouse's Gap Lemma : we…
Structural models with no solution are incoherent, and those with multiple solutions are incomplete. We show that models with occasionally binding constraints are not generically coherent. Coherency requires restrictions on the parameters…
Large language models (LLMs) often encounter knowledge conflicts, scenarios where discrepancy arises between the internal parametric knowledge of LLMs and non-parametric information provided in the prompt context. In this work we ask what…
Determining the validity of a quantified Boolean formula (QBF) is a PSPACE-complete problem with rich expressive power. Despite interest in efficient solvers, there is, compared to problems in NP, a lack of positive theoretical results, and…
FL$_\mathrm{ew}$-algebras form the algebraic semantics of the full Lambek calculus with exchange and weakening. We investigate two relations, called satisfiability and positive satisfiability, between FL$_\mathrm{ew}$-terms and…
In this work, we consider the satisfiability problem in a logic that combines word equations over string variables denoting words of unbounded lengths, regular languages to which words belong and Presburger constraints on the length of…
A critical variable of a satisfiable CNF formula is a variable that has the same value in all satisfying assignments. Using a simple case distinction on the fraction of critical variables of a CNF formula, we improve the running time for…
In this paper, we consider the multiplicity of solutions for a class of Kirchhoff type problems with sub-linear and critical terms on an unbounded domain. With the aid of Ekeland's variational principle and the concentration compactness…
We study parameterized Constraint Satisfaction Problem for infinite constraint languages. The parameters that we study are weight of the satisfying assignment, number of constraints, maximum number of occurrences of a variable in the…
We propose and study algorithms to compute minimal models, stable models and answer sets of t-CNF theories, and normal and disjunctive t-programs. We are especially interested in algorithms with non-trivial worst-case performance bounds.…
This note shows that under the unrestricted domain, there exists a choice liberal and Nash implementable social choice rule if and only if there are at least three players and the outcome set is at least twice as large as the player set. A…
Constraint "at most one" is a basic cardinality constraint which requires that at most one of its $n$ boolean inputs is set to $1$. This constraint is widely used when translating a problem into a conjunctive normal form (CNF) and we…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
The primary purpose of this article is to show that a certain natural set of axioms yields a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely)…
The satisfiability problem is NP-complete but there are subclasses where all the instances are satisfiable. For this, restrictions on the shape of the formula are made. Darman and D\"ocker show that the subclass MONOTONE $3$-SAT-($k$,1)…