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Existential rules have been proposed for representing ontological knowledge, specifically in the context of Ontology- Based Data Access. Entailment with existential rules is undecidable. We focus in this paper on conditions that ensure the…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
For linear recurrence systems, the problem of finding rational solutions is reduced to the problem of computing polynomial solutions by computing a content bound or a denominator bound. There are several bounds in the literature. The…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…
An efficient entailment proof system is essential to compositional verification using separation logic. Unfortunately, existing decision procedures are either inexpressive or inefficient. For example, Smallfoot is an efficient procedure but…
We study the asymptotics and fine-scale behavior of quantitative combinatorial measures of infinite words and related dynamical and algebraic structures. We construct infinite recurrent words $w$ whose complexity functions $p_w(n)$ are…
In this paper, we consider an approach introduced in term rewriting for the automatic detection of non-looping non-termination from patterns of rules. We adapt it to logic programming by defining a new unfolding technique that produces…
Recently Kubica et al. (Inf. Process. Let., 2013) and Kim et al. (submitted to Theor. Comp. Sci.) introduced order-preserving pattern matching. In this problem we are looking for consecutive substrings of the text that have the same "shape"…
The main aim of this paper is to document the performance of $p$-refinement with respect to maximum principles and the non-negative constraint. The model problem is (steady-state) anisotropic diffusion with decay (which is a second-order…
We introduce a sound and complete coinductive proof system for reachability properties in transition systems generated by logically constrained term rewriting rules over an order-sorted signature modulo builtins. A key feature of the…
Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative…
Large Reasoning Models (LRMs) employ reasoning to address complex tasks. Such explicit reasoning requires extended context lengths, resulting in substantially higher resource consumption. Prior work has shown that adversarially crafted…
This paper presents a theory of systemic undecidability, reframing incomputability as a structural property of systems rather than a localized feature of specific functions or problems. We define a notion of causal embedding and prove a…
We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating…
We describe various computational models based initially, but not exclusively, on that of the Turing machine, that are generalized to allow for transfinitely many computational steps. Variants of such machines are considered that have…
We study primary submodules and primary decompositions from a differential and computational point of view. Our main theoretical contribution is a general structure theory and a representation theorem for primary submodules of an arbitrary…
To answer database queries over incomplete data the gold standard is finding certain answers: those that are true regardless of how incomplete data is interpreted. Such answers can be found efficiently for conjunctive queries and their…
We study infinite words fixed by a morphism and their derived words. A derived word is a coding of return words to a factor. We exhibit two examples of sets of morphisms which are closed under derivation --- any derived word with respect to…
We study the growth behaviour of rational linear recurrence sequences. We show that for low-order sequences, divergence is decidable in polynomial time. We also exhibit a polynomial-time algorithm which takes as input a divergent rational…