{"title":"Weighted Context-Free Grammars Over Bimonoids","authors":"George Rahonis, Faidra Torpari","doi":"10.7561/SACS.2019.1.59","DOIUrl":null,"url":null,"abstract":"We introduce and investigate weighted context-free grammars over an arbitrary bimonoid K. Thus, we do not assume that the operations of K are commutative or idempotent or they distribute over each other. We prove a Chomsky-Schützenberger type theorem for the series generated by our grammars. Moreover, we show that the class of series generated by weighted right-linear grammars over a linearly ordered alphabet Σ and K coincides with that of recognizable series over Σ and K.","PeriodicalId":394919,"journal":{"name":"Sci. Ann. Comput. Sci.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Sci. Ann. Comput. Sci.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7561/SACS.2019.1.59","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We introduce and investigate weighted context-free grammars over an arbitrary bimonoid K. Thus, we do not assume that the operations of K are commutative or idempotent or they distribute over each other. We prove a Chomsky-Schützenberger type theorem for the series generated by our grammars. Moreover, we show that the class of series generated by weighted right-linear grammars over a linearly ordered alphabet Σ and K coincides with that of recognizable series over Σ and K.
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