{"title":"On the Sentence Valuations in a Semiring","authors":"Adrian Atanasiu, C. Martín-Vide, V. Mitrana","doi":"10.1142/9789812704979_0002","DOIUrl":"https://doi.org/10.1142/9789812704979_0002","url":null,"abstract":"This paper proposes an algebraic way of sentence valuations in a semiring. Actually, throughout the paper only valuations in the ring of integers with usual addition and multiplication are considered. These valuations take into consideration both words and their positions within the sentences. Two synonymy relations, with respect to a given valuation, are introduced. All sentences that are synonymous form a synonymy class. Some basic problems regarding the synonymy classes, which are actually formal languages, are formulated and studied. Some of them are completely solved whereas partial answers are provided for others. TUCS Research Group Theory Group: Mathematical Structures in Computer Science","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"66 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124661499","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}
{"title":"Acts over Right, Left Regular Bands and Semilattices Types","authors":"Tatsuhiko Saito","doi":"10.1142/9789812704979_0030","DOIUrl":"https://doi.org/10.1142/9789812704979_0030","url":null,"abstract":"Let S be a semigroup and let X be a non-empty set. Then X is called a right act over S or simply S-act if there is a mapping X x S 4 X , (2 , s) C) x s with the property ( x s ) t = x ( s t ) . A semigroup S is called a band if every element in S is an idempotent. A band S is called r ight regular (resp. l e f t regular) if sts = st (resp. sts = ts) holds for every s, t E S. A commutative band is called a semilatt ice. An S-act X is said to be a right regular band type, or simply RRB-type, if xs2 = x s and x s t s = x s t for all x E X and every s, t E S. A left regular band type (LRB-type) S-act and a semilattice type (SL-type) S-act are similarly defined. When S is a free monoid a RRB-type automaton, an LRB-type automaton and an SL-type auromaton can be similarly defined. In this case, for an automaton A = (A, X , a), where A is an alphabet, X is a set of states and 6 is a mapping X x A -+ X , ( 2 , a) C) xu. we can show that, if xu2 = za and xaba = xab for all x E X , a , b E A, then xs2 = x s and x s t s = x for all x E X, s, t E A*. This fact can be applied to LRB-type automata and SL-type automata. Our purpose is to determine all S-act which are right regular band types, left regular band types and semilattice types, respectively. To achieve the purpose, we obtain necessary and sufficient conditions, for any given set X , and any semigroup S, in order that X is S-acts which are a RRB-type, a LRB-type and a SL-type, respectively (Theorems 1,3,5). Further we obtain more concrete results to construct actually RRB-type, LRB-type and SGtype automata, respectively (Corollaries 2,4,5). Let X be a S-act. It is well-known that defining a relation p on S by spt if x s = x t for all x E X . a transformation semigroup S/p on X can be obtained. Thus, from the above results, every right regular band, left regular band and semilattce can be obtained in the full transformation semigroup T ( X ) , respectively.","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124519598","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}
{"title":"On A Class of Hypercodes","authors":"Do Long Van","doi":"10.1142/9789812704979_0012","DOIUrl":"https://doi.org/10.1142/9789812704979_0012","url":null,"abstract":"","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"2011 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127359387","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}
{"title":"Join Decompositions of Pseudovarieties of the Form DH ECom","authors":"K. Auinger","doi":"10.1142/9789812704979_0003","DOIUrl":"https://doi.org/10.1142/9789812704979_0003","url":null,"abstract":"","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133680274","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}
{"title":"Cellular Automata with Polynomials over Finite Fields","authors":"H. Nishio","doi":"10.1142/9789812704979_0028","DOIUrl":"https://doi.org/10.1142/9789812704979_0028","url":null,"abstract":"","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117242995","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}
{"title":"The Emperor's New Recursiveness: The Epigraph of the Exponential Function in Two Models of Computability","authors":"V. Brattka","doi":"10.1142/9789812704979_0005","DOIUrl":"https://doi.org/10.1142/9789812704979_0005","url":null,"abstract":"In his book The Emperor’s New Mind\" Roger Penrose implicitly denes some criteria which should be met by a reasonable notion of recursiveness for subsets of Euclidean space. We discuss two such notions with regard to Penrose’s criteria: one originated from computable analysis, and the one introduced by Blum, Shub and Smale.","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134114542","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}
{"title":"Tree Automata in the Theory of Term Rewriting","authors":"M. Steinby","doi":"10.1142/9789812704979_0034","DOIUrl":"https://doi.org/10.1142/9789812704979_0034","url":null,"abstract":"","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121434476","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}
{"title":"Presentations of Right Unitary Submonoids of Monoids","authors":"Isamu Inata","doi":"10.1142/9789812704979_0017","DOIUrl":"https://doi.org/10.1142/9789812704979_0017","url":null,"abstract":"","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125450357","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}
{"title":"Subdirect Product Structure of Left Clifford Semigroups","authors":"K. Shum, M. Sen, Y. Guo","doi":"10.1142/9789812704979_0033","DOIUrl":"https://doi.org/10.1142/9789812704979_0033","url":null,"abstract":"","PeriodicalId":265391,"journal":{"name":"Words, Languages & Combinatorics","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2003-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128231949","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}
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
