Mathematical Structures in Computer Science最新文献_第8页

Confluence of left-linear higher-order rewrite theories by checking their nested critical pairs 用嵌套临界对检验左线性高阶重写理论的合流性

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-03-17 DOI: 10.1017/S0960129522000044

Gilles Dowek, Gaspard Férey, J. Jouannaud, Jiaxiang Liu

{"title":"Confluence of left-linear higher-order rewrite theories by checking their nested critical pairs","authors":"Gilles Dowek, Gaspard Férey, J. Jouannaud, Jiaxiang Liu","doi":"10.1017/S0960129522000044","DOIUrl":"https://doi.org/10.1017/S0960129522000044","url":null,"abstract":"Abstract User-defined higher-order rewrite rules are becoming a standard in proof assistants based on intuitionistic type theory. This raises the question of proving that they preserve the properties of beta-reductions for the corresponding type systems. In a series of papers, we develop techniques based on van Oostrom’s decreasing diagrams that reduce confluence proofs to the checking of various forms of critical pairs for higher-order rewrite rules extending beta-reduction on pure lambda-terms. As shown in a previous paper of the two middle authors, confluence of a terminating set of left-linear rewrite rules is obtained when their critical pairs are joinable, beta-rewrite steps being disallowed. The present paper concentrates on the case where arbitrary beta-rewrite steps are allowed for joining critical pairs. The rewrite relation used for analyzing confluence may rewrite arbitrarily many non-overlapping redexes in a single step. This relation gives rise to critical pairs that overlap both horizontally, as with parallel rewriting, but also vertically, forming chains of successive overlaps. Practical examples of use of this technique are analyzed.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"898 - 933"},"PeriodicalIF":0.5,"publicationDate":"2022-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44418770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Two decades of automatic amortized resource analysis 二十年的自动摊销资源分析

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-03-16 DOI: 10.1017/S0960129521000487

Jan Hoffmann, Steffen Jost

引用次数: 3

On Petrie cycle and Petrie tour partitions of 3- and 4-regular plane graphs 关于3-和4-正则平面图的Petrie环和Petrie tour划分

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-02-01 DOI: 10.1017/S0960129522000238

Xin He, Huaming Zhang, Yijie Han

{"title":"On Petrie cycle and Petrie tour partitions of 3- and 4-regular plane graphs","authors":"Xin He, Huaming Zhang, Yijie Han","doi":"10.1017/S0960129522000238","DOIUrl":"https://doi.org/10.1017/S0960129522000238","url":null,"abstract":"Abstract Given a plane graph \u0000$G=(V,E)$\u0000 , a Petrie tour of G is a tour P of G that alternately turns left and right at each step. A Petrie tour partition of G is a collection \u0000${mathscr P}={P_1,ldots,P_q}$\u0000 of Petrie tours so that each edge of G is in exactly one tour \u0000$P_i in {mathscr P}$\u0000 . A Petrie tour P is called a Petrie cycle if all its vertices are distinct. A Petrie cycle partition of G is a collection \u0000${mathscr C}={C_1,ldots,C_p}$\u0000 of Petrie cycles so that each vertex of G is in exactly one cycle \u0000$C_i in {mathscr C}$\u0000 . In this paper, we study the properties of 3-regular plane graphs that have Petrie cycle partitions and 4-regular plane multi-graphs that have Petrie tour partitions. Given a 4-regular plane multi-graph \u0000$G=(V,E)$\u0000 , a 3-regularization of G is a 3-regular plane graph \u0000$G_3$\u0000 obtained from G by splitting every vertex \u0000$vin V$\u0000 into two degree-3 vertices. G is called Petrie partitionable if it has a 3-regularization that has a Petrie cycle partition. The general version of this problem is motivated by a data compression method, tristrip, used in computer graphics. In this paper, we present a simple characterization of Petrie partitionable graphs and show that the problem of determining if G is Petrie partitionable is NP-complete.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"240 - 256"},"PeriodicalIF":0.5,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46159547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Synchronizing words and monoid factorization, yielding a new parameterized complexity class? 同步单词和monoid因子分解，产生一个新的参数化复杂度类？

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-02-01 DOI: 10.1017/S0960129522000184

H. Fernau, Jens Bruchertseifer

引用次数: 1

Rogers semilattices of punctual numberings 准时编号的罗杰斯半格

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-02-01 DOI: 10.1017/S0960129522000093

N. Bazhenov, M. Mustafa, S. Ospichev

引用次数: 0

Hofmann-Mislove type definitions of non-Hausdorff spaces 非Hausdorff空间的Hofman-Mislove型定义

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-01-01 DOI: 10.1017/S0960129522000196

Chong Shen, Xiaoyong Xi, Xiaoquan Xu, Dongsheng Zhao

{"title":"Hofmann-Mislove type definitions of non-Hausdorff spaces","authors":"Chong Shen, Xiaoyong Xi, Xiaoquan Xu, Dongsheng Zhao","doi":"10.1017/S0960129522000196","DOIUrl":"https://doi.org/10.1017/S0960129522000196","url":null,"abstract":"Abstract One of the most important results in domain theory is the Hofmann-Mislove Theorem, which reveals a very distinct characterization for the sober spaces via open filters. In this paper, we extend this result to the d-spaces and well-filtered spaces. We do this by introducing the notions of Hofmann-Mislove-system (HM-system for short) and \u0000$Psi$\u0000 -well-filtered space, which provide a new unified approach to sober spaces, well-filtered spaces, and d-spaces. In addition, a characterization for \u0000$Psi$\u0000 -well-filtered spaces is provided via \u0000$Psi$\u0000 -sets. We also discuss the relationship between \u0000$Psi$\u0000 -well-filtered spaces and H-sober spaces considered by Xu. We show that the category of complete \u0000$Psi$\u0000 -well-filtered spaces is a full reflective subcategory of the category of \u0000$T_0$\u0000 spaces with continuous mappings. For each HM-system \u0000$Psi$\u0000 that has a designated property, we show that a \u0000$T_0$\u0000 space X is \u0000$Psi$\u0000 -well-filtered if and only if its Smyth power space \u0000$P_s(X)$\u0000 is \u0000$Psi$\u0000 -well-filtered.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"111 - 124"},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49542231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Proof-relevance in Bishop-style constructive mathematics 毕晓普式构造数学中的证明相关性

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-01-01 DOI: 10.1017/S0960129522000159

I. Petrakis

{"title":"Proof-relevance in Bishop-style constructive mathematics","authors":"I. Petrakis","doi":"10.1017/S0960129522000159","DOIUrl":"https://doi.org/10.1017/S0960129522000159","url":null,"abstract":"Abstract Bishop’s presentation of his informal system of constructive mathematics BISH was on purpose closer to the proof-irrelevance of classical mathematics, although a form of proof-relevance was evident in the use of several notions of moduli (of convergence, of uniform continuity, of uniform differentiability, etc.). Focusing on membership and equality conditions for sets given by appropriate existential formulas, we define certain families of proof sets that provide a BHK-interpretation of formulas that correspond to the standard atomic formulas of a first-order theory, within Bishop set theory \u0000$(mathrm{BST})$\u0000 , our minimal extension of Bishop’s theory of sets. With the machinery of the general theory of families of sets, this BHK-interpretation within BST is extended to complex formulas. Consequently, we can associate to many formulas \u0000$phi$\u0000 of BISH a set \u0000${texttt{Prf}}(phi)$\u0000 of “proofs” or witnesses of \u0000$phi$\u0000 . Abstracting from several examples of totalities in BISH, we define the notion of a set with a proof-relevant equality, and of a Martin-Löf set, a special case of the former, the equality of which corresponds to the identity type of a type in intensional Martin-Löf type theory \u0000$(mathrm{MLTT})$\u0000 . Through the concepts and results of BST notions and facts of MLTT and its extensions (either with the axiom of function extensionality or with Vooevodsky’s axiom of univalence) can be translated into BISH. While Bishop’s theory of sets is standardly understood through its translation to MLTT, our development of BST offers a partial translation in the converse direction.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"32 1","pages":"1 - 43"},"PeriodicalIF":0.5,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46111842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Implicit computation complexity in higher-order programming languages: A Survey in Memory of Martin Hofmann 高阶编程语言的隐式计算复杂性:马丁·霍夫曼的记忆综述

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-01-01 DOI: 10.1017/S0960129521000505

Ugo Dal Lago

引用次数: 2

The role of linearity in sharing analysis 线性在共享分析中的作用

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2022-01-01 DOI: 10.1017/S0960129522000160

G. Amato, M. Meo, F. Scozzari

引用次数: 1

Cubical methods in homotopy type theory and univalent foundations 同伦型理论中的三次方法及一元基础

IF 0.5 4区计算机科学

Mathematical Structures in Computer Science Pub Date : 2021-12-10 DOI: 10.1017/s0960129521000311

Anders Mörtberg

{"title":"Cubical methods in homotopy type theory and univalent foundations","authors":"Anders Mörtberg","doi":"10.1017/s0960129521000311","DOIUrl":"https://doi.org/10.1017/s0960129521000311","url":null,"abstract":"\u0000 Cubical methods have played an important role in the development of Homotopy Type Theory and Univalent Foundations (HoTT/UF) in recent years. The original motivation behind these developments was to give constructive meaning to Voevodsky’s univalence axiom, but they have since then led to a range of new results. Among the achievements of these methods is the design of new type theories and proof assistants with native support for notions from HoTT/UF, syntactic and semantic consistency results for HoTT/UF, as well as a variety of independence results and establishing that the univalence axiom does not increase the proof theoretic strength of type theory. This paper is based on lecture notes that were written for the 2019 Homotopy Type Theory Summer School at Carnegie Mellon University. The goal of these lectures was to give an introduction to cubical methods and provide sufficient background in order to make the current research in this very active area of HoTT/UF more accessible to newcomers. The focus of these notes is hence on both the syntactic and semantic aspects of these methods, in particular on cubical type theory and the various cubical set categories that give meaning to these theories.","PeriodicalId":49855,"journal":{"name":"Mathematical Structures in Computer Science","volume":"15 1","pages":"1147-1184"},"PeriodicalIF":0.5,"publicationDate":"2021-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88929140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1