Computability最新文献

Computability Pub Date : 2024-04-12 DOI: 10.3233/com-230471

Patrick Uftring

引用次数: 0

Choice principles characterizing the difference between König’s lemma and weak König’s lemma in constructive reverse mathematics 表征构造反向数学中柯尼希两难和弱柯尼希两难之间差异的选择原则

Computability Pub Date : 2024-04-02 DOI: 10.3233/com-230478

Makoto Fujiwara, Takako Nemoto

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Computing the index of non-isometric k-ary words with Hamming and Lee distance 用 Hamming 和 Lee 距离计算非等距 k 字词的索引

Computability Pub Date : 2024-03-01 DOI: 10.3233/com-230441

M. Anselmo, Manuela Flores, Maria Madonia

{"title":"Computing the index of non-isometric k-ary words with Hamming and Lee distance","authors":"M. Anselmo, Manuela Flores, Maria Madonia","doi":"10.3233/com-230441","DOIUrl":"https://doi.org/10.3233/com-230441","url":null,"abstract":"Isometric words are those words whose occurrence as a factor in a transformation of a word u in a word v can be avoided, while preserving the minimal length of the transformation. Such minimal length refers to a distance between u and v. In the literature, isometric words have been considered with respect to the Hamming distance and the Lee distance; the former especially for binary words, while the latter for k-ary words, with k ⩾ 2. Ham- and Lee- isometric words have been characterized in terms of their overlaps with errors. In this paper, we give algorithms to decide whether a word f, of length n, is Ham- or Lee-isometric and provide evidence of the possible non-isometricity by returning a pair of words of minimal length whose transformation cannot avoid the factor f. Such a pair of words is called a pair of witnesses and the minimal length of the witnesses is called the index of f. The algorithms run in O ( n ) time with a preprocessing of O ( n ) time and space to construct a data structure that allows answering LCA queries on the suffix tree of f in constant time. The correctness of the algorithms lies on some theoretical results on the index and the witnesses of a word that are here presented. The investigation on the index is completed by the characterization of words with minimum/maximum index. All the results are shown referring to both Hamming and Lee distance.","PeriodicalId":515920,"journal":{"name":"Computability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140091350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Complemented subsets and Boolean-valued, partial functions 补全子集和布尔值部分函数

Computability Pub Date : 2024-02-14 DOI: 10.3233/com-230462

Daniel Misselbeck-Wessel, I. Petrakis

{"title":"Complemented subsets and Boolean-valued, partial functions","authors":"Daniel Misselbeck-Wessel, I. Petrakis","doi":"10.3233/com-230462","DOIUrl":"https://doi.org/10.3233/com-230462","url":null,"abstract":"We study the two algebras of complemented subsets that were introduced in the constructive development of the Daniell approach to measure and integration within Bishop-style constructive mathematics. We present their main properties both for the so-called here categorical complemented subsets and for the extensional complemented subsets. We translate constructively the classical bijection between subsets and Boolean-valued, total functions by establishing a bijection between complemented subsets (categorical or extensional) and Boolean-valued, partial functions (categorical or extensional). The role of Myhill’s axiom of non-choice in the equivalence between categorical and extensional subsets is discussed. We introduce swap algebras of type (I) and (II) as an abstract version of Bishop’s algebras of complemented subsets of type (I) and (II), respectively, and swap rings as an abstract version of the structure of Boolean-valued partial functions on a set. Our examples of swap algebras and swap rings together with the included here results indicate that their theory is a certain generalisation of the theory of Boolean algebras and Boolean rings, a fact which we find interesting both from a constructive and a classical point of view.","PeriodicalId":515920,"journal":{"name":"Computability","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139963789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1