Related papers: On Algebraic Abstractions for Concurrent Separatio…
A formal context consists of objects, properties, and the incidence relation between them. Various notions of concepts defined with respect to formal contexts and their associated algebraic structures have been studied extensively,…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
This paper is divided into two parts. The first is a review, through categorical lenses, of the classical theory of regular-singular differential systems over $C((x))$ and $\mathbb P^1_C\smallsetminus\{0,\infty\}$, where $C$ is…
The theory of program modules is of interest to language designers not only for its practical importance to programming, but also because it lies at the nexus of three fundamental concerns in language design: the phase distinction,…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
We introduce the normal produoidal category of monoidal contexts over an arbitrary monoidal category. In the same sense that a monoidal morphism represents a process, a monoidal context represents an incomplete process: a piece of a…
The notion of homomorphism indistinguishability offers a combinatorial framework for characterizing equivalence relations of graphs, in particular equivalences in counting logics within finite model theory. That is, for certain graph…
We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…
Learning latent representations from complex data is central to modern machine learning, spanning temporal, multimodal, and partially observed systems. In such settings, representations are better understood as latent states capturing…
Iterative abstraction refinement techniques are one of the most prominent paradigms for the analysis and verification of systems with large or infinite state spaces. This paper investigates the changes of truth values of system properties…
We investigate the extent to which modern, neural language models are susceptible to structural priming, the phenomenon whereby the structure of a sentence makes the same structure more probable in a follow-up sentence. We explore how…
To preserve previously learned representations, continual learning systems must strike a balance between plasticity, the ability to acquire new knowledge, and stability. This stability-plasticity dilemma affects how representations can be…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
We introduce a formalism based on a combinatorial notion of cell complex subject to an inclusion-reversing duality operation. Our main goal is to open the way for a functorial definition of field theories in a context where no manifold or…
The verification community has studied dynamic data structures primarily in a bottom-up way by analyzing pointers and the shapes induced by them. Recent work in fields such as separation logic has made significant progress in extracting…
Often in Software Engineering, a modeling formalism has to support scenarios of inconsistency in which several requirements either reinforce or contradict each other. Paraconsistent transition systems are proposed in this paper as one such…
Functional decomposition of logic circuits has profound influence on all quality aspects of the cost-effective implementation of modern digital systems. In this paper, a relational approach to the decomposition of logic circuits is…
Uniform coloured Petri nets can be abstracted to their skeleton, the place/transition net that simply turns the coloured tokens into black tokens. A coloured net and its skeleton are related by a net morphism. For the application of the…
Semigroup theory is a branch of abstract algebra, and it provides mathematical tools for the theory of computation. Finite semigroups can describe state transition systems and thus they model physically realizable computers. Engineering…