相关论文: Distributive Computability
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
In [Ben13], the notion of logically distributive category has been introduced to provide a sound and complete semantics to multi-sorted first-order logical theories based on intuitionistic logic. In this note, it will be shown that the…
This work emphasizes the assets of implementing the distributed computing for the intensive use in computational science devoted to the search of new medicines that could be applied in public healthy problems.
We propose a definition of quantum computable functions as mappings between superpositions of natural numbers to probability distributions of natural numbers. Each function is obtained as a limit of an infinite computation of a quantum…
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory, by showing that for every nontrivial countable structure S,…
This thesis develops the translation between category theory and computational linguistics as a foundation for natural language processing. The three chapters deal with syntax, semantics and pragmatics. First, string diagrams provide a…
Probabilistic programming is becoming increasingly popular thanks to its ability to specify problems with a certain degree of uncertainty. In this work, we focus on term rewriting, a well-known computational formalism. In particular, we…
Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming…
Computability theory is a discipline in the intersection of computer science and mathematical logic where the fundamental question is: given two mathematical objects X and Y, does X compute Y in principle? In case X and Y are real numbers,…
Paper describes the theoretical and practical aspects of the proposed model that uses distributed computing to a global network of Internet communication. Distributed computing are widely used in modern solutions such as research, where the…
This work establishes the fundamental limits of the classical problem of multi-user distributed computing of linearly separable functions. In particular, we consider a distributed computing setting involving $L$ users, each requesting a…
We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes, with bounded computation and storage capabilities that do not scale with the network size. Our goal is to characterize the…
We present a survey of some developments in the general area of category-theoretic approaches to the theory of computation, with a focus on topics and ideas particularly close to the interests of Jim Lambek.
Computational problems are classified into computable and uncomputable problems. If there exists an effective procedure (algorithm) to compute a problem then the problem is computable otherwise it is uncomputable. Turing machines can…
We describe a dynamic programming algorithm for computing the marginal distribution of discrete probabilistic programs. This algorithm takes a functional interpreter for an arbitrary probabilistic programming language and turns it into an…
Large language models (LLM) are advanced AI systems trained on extensive textual data, leveraging deep learning techniques to understand and generate human-like language. Today's LLMs with billions of parameters are so huge that hardly any…
This paper summarises the current state-of-the art in the study of compositionality in distributional semantics, and major challenges for this area. We single out generalised quantifiers and intensional semantics as areas on which to focus…
Categorical random variables are a common staple in machine learning methods and other applications across disciplines. Many times, correlation within categorical predictors exists, and has been noted to have an effect on various algorithm…
A classical method for partition generating functions is developed into a tool with wide applications. New expansions of well-known theorems are derived, and new results for partitions with n copies of n are presented.
Generalising slightly the notions of a strict computability model and of a simulation between them, which were elaborated by Longley and Normann, we define canonical computability models over categories and appropriate Set-valued functors…