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The goal of this paper is to establish that it remains undecidable whether a sequent is provable in two systems in which a weakening rule for an exponential modality is completely omitted from classical propositional linear logic…

Logic in Computer Science · Computer Science 2025-09-03 Jun Suzuki , Katsuhiko Sano

Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of…

Quantum Physics · Physics 2026-03-17 Serge Massar

We consider entailment problems involving powerful constraint languages such as guarded existential rules, in which additional semantic restrictions are put on a set of distinguished relations. We consider restricting a relation to be…

Databases · Computer Science 2019-03-21 Antoine Amarilli , Michael Benedikt , Pierre Bourhis , Michael Vanden Boom

We prove the undecidability of MSO on $\omega$-words extended with the second-order predicate $U_1(X)$ which says that the distance between consecutive positions in a set $X \subseteq \mathbb{N}$ is unbounded. This is achieved by showing…

Logic in Computer Science · Computer Science 2023-06-22 Mikołaj Bojańczyk , Laure Daviaud , Bruno Guillon , Vincent Penelle , A. V. Sreejith

We study systems of polynomial equations in infinite finitely generated commutative associative rings with an identity element. For each such ring $R$ we obtain an interpretation by systems of equations of a ring of integers $O$ of a finite…

Number Theory · Mathematics 2021-02-08 Albert Garreta , Alexei Miasnikov , Denis Ovchinnikov

The article proposes a new technique for proving the undefinability of logical connectives through each other and illustrates the technique with several examples. Some of the obtained results are new proofs of the existing theorems, others…

Artificial Intelligence · Computer Science 2023-07-04 Sophia Knight , Pavel Naumov , Qi Shi , Vigasan Suntharraj

Recently it has been proved that, assuming that there is an almost disjoint family of cardinality (2^{\mathfrak c}) in (\mathfrak c) (which is assured, for instance, by either Martin's Axiom, or CH, or even $2^{<\mathfrak c=\mathfrak c$})…

Functional Analysis · Mathematics 2012-07-13 Jose Luis Gamez-Merino , Juan B. Seoane-Sepulveda

We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…

Logic in Computer Science · Computer Science 2022-02-18 Antoine Amarilli , Michael Benedikt , Pierre Bourhis , Michael Vanden Boom

In this paper, we extend the notion of Lyndon word to transfinite words. We prove two main results. We first show that, given a transfinite word, there exists a unique factorization in Lyndon words that are densely non-increasing, a…

Formal Languages and Automata Theory · Computer Science 2023-06-22 Olivier Carton , Luc Boasson

Is there a fixed dimension $n$ such that translational tiling of $\mathbb{Z}^n$ with a monotile is undecidable? Several recent results support a positive answer to this question. Greenfeld and Tao disprove the periodic tiling conjecture by…

Combinatorics · Mathematics 2024-12-17 Chan Yang , Zhujun Zhang

The problem of linking the structure of a finite linear dynamical system with its dynamics is well understood when the phase space is a vector space over a finite field. The cycle structure of such a system can be described by the…

Dynamical Systems · Mathematics 2008-10-20 Guangwu Xu , Yi Ming Zou

Finite (word) state transducers extend finite state automata by defining a binary relation over finite words, called rational relation. If the rational relation is the graph of a function, this function is said to be rational. The class of…

Formal Languages and Automata Theory · Computer Science 2025-04-25 Emmanuel Filiot , Ismaël Jecker , Khushraj Madnani , Saina Sunny

Motivated by an application where we try to make proofs for Description Logic inferences smaller by rewriting, we consider the following decision problem, which we call the small term reachability problem: given a term rewriting system $R$,…

Logic in Computer Science · Computer Science 2025-10-22 Franz Baader , Jürgen Giesl

The paper studies constructions of irreducible polynomials over finite fields using polynomial composition method.

Number Theory · Mathematics 2010-08-12 Melsik K. Kyuregyan , Gohar M. Kyureghyan

We solve a well known, long-standing open problem in relational databases theory, showing that the conjunctive query determinacy problem (in its "unrestricted" version) is undecidable.

Databases · Computer Science 2015-12-08 Tomasz Gogacz , Jerzy Marcinkowski

We give two elementary proofs, at a level understandable by students with only pre-calculus knowledge of Algebra, of the well known fact that an irreducible irrational n-th root of a positive rational number cannot be solution of a…

History and Overview · Mathematics 2009-08-04 S. A. Belbas

We define two new families of polynomials that generalize permanents and prove upper and lower bounds on their determinantal complexities comparable to the known bounds for permanents. One of these families is obtained by replacing…

Combinatorics · Mathematics 2022-03-01 Tristram Bogart , Juan Andrés Valero

Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…

Number Theory · Mathematics 2024-01-01 Ruikai Chen , Sihem Mesnager

All known structural extensions of the substructural logic $\mathsf{FL_e}$, Full Lambek calculus with exchange/commutativity, (corresponding to subvarieties of commutative residuated lattices axiomatized by $\{\vee, \cdot, 1\}$-equations)…

Logic · Mathematics 2023-10-04 Nikolaos Galatos , Gavin St. John

Due to the undecidability of most type-related properties of System F like type inhabitation or type checking, restricted polymorphic systems have been widely investigated (the most well-known being ML-polymorphism). In this paper we…

Logic in Computer Science · Computer Science 2021-05-04 Paolo Pistone , Luca Tranchini