相关论文: Categorical Semantics of Reversible Pattern-Matchi…

This paper provides a geometric characterization of subclasses of the regular languages. We use finite model theory to characterize objects like strings and trees as relational structures. Logical statements meeting certain criteria over…

Today, reusable components are available in several repositories. These last are certainly conceived for the reusing However, this re-use is not immediate; it requires, in the fact, to pass through some essential conceptual operations,…

Session types provide guarantees about concurrent behaviour and can be understood through their correspondence with linear logic, with propositions as sessions and proofs as processes. However, a strictly linear setting is somewhat…

Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…

We study properties of the category of modules of an algebra object A in a tensor category C. We show that the module category inherits various structures from C, provided that A is a Frobenius algebra with certain additional properties. As…

Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…

Neural networks excel at pattern recognition but struggle with reliable logical reasoning, often violating basic logical principles during inference. We address this limitation by developing a categorical framework that systematically…

Turing's famous 'machine' framework provides an intuitively clear conception of 'computing with real numbers'. A recursive counterexample to a theorem shows that the theorem does not hold when restricted to computable objects. These…

A relational structure $\mathbb{X}$ is called reversible iff each bijective homomorphism from $\mathbb{X}$ onto $\mathbb{X}$ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible…

Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…

Automated generation of high-quality topical hierarchies for a text collection is a dream problem in knowledge engineering with many valuable applications. In this paper a scalable and robust algorithm is proposed for constructing a…

Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been…

In the past years, software reverse engineering dealt with source code understanding. Nowadays, it is levered to software requirements abstract level, supported by feature model notations, language independent, and simpler than the source…

Program equivalence is the fulcrum for reasoning about and proving properties of programs. For noninterference, for example, program equivalence up to the secrecy level of an observer is shown. A powerful enabler for such proofs are logical…

We introduce the notion of a categorical join, which can be thought of as a categorification of the classical join of two projective varieties. This notion is in the spirit of homological projective duality, which categorifies classical…

We present a deep hierarchical recurrent neural network for sequence tagging. Given a sequence of words, our model employs deep gated recurrent units on both character and word levels to encode morphology and context information, and…

This work examines approaches to making computational models reversible. Broadly speaking, transforming a computational model into a reversible one, i.e. reversibilizing it, means extending its operational semantics conservatively in a way…

Reynolds' parametricity originally equips types with proof-irrelevant binary propositional relations over the types. But such relations can also be taken proof-relevant or unary, and described either in an indexed or fibred way.…

Session types model structured communication-based programming. In particular, binary session types for the pi-calculus describe communication between exactly two participants in a distributed scenario. Adding sessions to the pi-calculus…

For any cssc-crossed module a category is constructed, equipped with a structure and proved that this is a coherent categorical group. Together with a result of the previous paper, where to any categorical group the cssc-crossed module is…