{"title":"Weighted two-way transducers","authors":"Fan Feng, Andreas Maletti","doi":"10.1016/j.ic.2023.105094","DOIUrl":null,"url":null,"abstract":"<div><p>Weighted two-way transducers over complete commutative semirings are introduced and investigated. Their computed mappings have two-way definable support. Conversely, for every two-way definable relation <em>R</em> there exists a mapping that has support <em>R</em><span> and is computable by a weighted two-way transducer. The class of all such computed mappings is naturally closed under sum. Finally, both the subclass computed by deterministic weighted two-way transducers and the subclass computed by unambiguous weighted two-way transducers are shown to be closed under composition, pseudo </span><span>Hadamard</span> product, unambiguous <span>Cauchy</span> product, and unambiguous <span>Kleene</span> iteration.</p></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"295 ","pages":"Article 105094"},"PeriodicalIF":0.8000,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Information and Computation","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0890540123000974","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Weighted two-way transducers over complete commutative semirings are introduced and investigated. Their computed mappings have two-way definable support. Conversely, for every two-way definable relation R there exists a mapping that has support R and is computable by a weighted two-way transducer. The class of all such computed mappings is naturally closed under sum. Finally, both the subclass computed by deterministic weighted two-way transducers and the subclass computed by unambiguous weighted two-way transducers are shown to be closed under composition, pseudo Hadamard product, unambiguous Cauchy product, and unambiguous Kleene iteration.
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Information and Computation welcomes original papers in all areas of theoretical computer science and computational applications of information theory. Survey articles of exceptional quality will also be considered. Particularly welcome are papers contributing new results in active theoretical areas such as
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