相关论文: A Categorical Theory of Patches

Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…

In this paper we consider the problem of `theory patching', in which we are given a domain theory, some of whose components are indicated to be possibly flawed, and a set of labeled training examples for the domain concept. The theory…

Automated program repair is a problem of finding a transformation (called a patch) of a given incorrect program that eliminates the observable failures. It has important applications such as providing debugging aids, automatically grading…

We demonstrate how category theory provides specifications that can efficiently be implemented via imperative algorithms and apply this to the field of graph rewriting. By examples, we show how this paradigm of software development makes it…

Software patching is a common method of removing vulnerabilities in software components to make IT systems more secure. However, there are many cases where software patching is not possible due to the critical nature of the application,…

Some aspects of basic category theory are developed in a finitely complete category $\C$, endowed with two factorization systems which determine the same discrete objects and are linked by a simple reciprocal stability law. Resting on this…

A version control system, such as Git, requires a way to integrate changes from different developers or branches. Given a merge scenario, a merge tool either outputs a clean integration of the changes, or it outputs a conflict for manual…

Developing complex software requires that multiple views and versions of the software can be developed in parallel and merged as supported by views and managed by version control systems. In this context, this paper considers monitoring…

This paper explores the interplay between category theory, topology, and the algebraic theory of finite groups. Our analysis unfolds in three stages. First, we establish the foundational universe of our objects: the complete and cocomplete…

In this article, we propose a Category Theory approach to (syntactic) interoperability between linguistic tools. The resulting category consists of textual documents, including any linguistic annotations, NLP tools that analyze texts and…

In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…

The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…

This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…

Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…

Data reconciliation in general, and filesystem synchronization in particular, lacks rigorous theoretical foundation. This paper presents, for the first time, a complete analysis of synchronization for two replicas of a theoretical…

Data integration and migration processes in polystores and multi-model database management systems highly benefit from data and schema transformations. Rigorous modeling of transformations is a complex problem. The data and schema…

Unlike static documents, version-controlled documents are edited by one or more authors over a certain period of time. Examples include large scale computer code, papers authored by a team of scientists, and online discussion boards. Such…

Since the seminal work from F. Cohen in the eighties, abstract virology has seen the apparition of successive viral models, all based on Turing-equivalent formalisms. But considering recent malware such as rootkits or k-ary codes, these…

A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…

The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…