Monoidal computer I: 文字列図による基本的な計算可能性
Monoidal computer I: Basic computability by string diagrams (2012) (arxiv.org)
要約
本論文では、モノイダル圏の観点から計算の新しいモデルを提案しています。このモデルはチャーチ＝チューリングのテーゼに準拠し、標準的なモデルと同じ計算可能関数を捉えます。特に、計算の意味論とプログラミングの研究から生まれた構造を利用し、抽象的な推論のための具体的で直感的なインターフェースを提供する文字列図というグラフィカルな形式をサポートしています。
全文翻訳
Computer Science > Logic in Computer Science
arXiv:1208.5205 (cs)
[Submitted on 26 Aug 2012 (v1), last revised 29 Dec 2012 (this version, v2)]
Title:Monoidal computer I: Basic computability by string diagrams
Authors:Dusko Pavlovic
View a PDF of the paper titled Monoidal computer I: Basic computability by string diagrams, by Dusko Pavlovic
Abstract:We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most of them, free of their diverse implementation details, using the ideas and structures that in the meantime emerged from research in semantics of computation and programming. The salient feature of the language of monoidal categories is that it is supported by a sound and complete graphical formalism, string diagrams, which provide a concrete and intuitive interface for abstract reasoning about computation. The original motivation and the ultimate goal of this effort is to provide a convenient high level programming language for a theory of computational resources, such as one-way functions, and trapdoor functions, by adopting the methods for hiding the low level implementation details that emerged from practice. In the present paper, we make a first step towards this ambitious goal, and sketch a path to reach it. This path is pursued in three sequel papers, that are in preparation.
| Comments: | 37 pages, 47 figures, Oxford Workshop on Resources in Security, July 2012; in this version: fixed typos, added a sentence to the abstract; accepted for publication in Information and Computation |
| Subjects: | Logic in Computer Science (cs.LO); Category Theory (math.CT) |
| MSC classes: | 03D10, 68Q05, 68Q15 |
| ACM classes: | F.1.1; F.1.3; F.4.1 |
| Cite as: | arXiv:1208.5205 [cs.LO] |
| (or arXiv:1208.5205v2 [cs.LO] for this version) | |
| https://doi.org/10.48550/arXiv.1208.5205 arXiv-issued DOI via DataCite | |
| Journal reference: | Information and Computation (2013) |
Submission history
From: Dusko Pavlovic
v1 Sun, 26 Aug 2012 08:47:16 UTC (1,199 KB)
[v2] Sat, 29 Dec 2012 13:07:13 UTC (1,199 KB)
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