Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0002
Adrian Atanasiu, C. Martín-Vide, V. Mitrana
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
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Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0030
Tatsuhiko Saito
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.
设S是一个半群，X是一个非空集合。如果存在一个映射X X S 4x， (2, S) C) X S具有(X S) t = X (S t)的性质，那么X就被称为S上的右行为或简称为S行为。如果半群S中的每一个元素都是幂等的，则称之为带。波段S称为右正则波段。如果STS = st (resp.)sts = ts)对每一个s, t E s都成立。一个可交换带被称为半冰。一个s -行为X被称为右正则带型，或简称rrb型，如果xs2 = X s和X s t s = X s t对于所有的X E X和每一个s, t E s。一个左正则带型(lrb -型)s -行为和半晶格型(sl -型)s -行为的定义类似。当S是rrb型自动机的自由单oid时，lrb型自动机和sl型自动机可以类似地定义。在这种情况下，对于自动机A = (A, X, A)，其中A是字母表，X是状态集合，6是映射X X A -+ X， (2, A) C) xu。我们可以证明，如果xx2 = za xaba = xab对于所有的x ex, a, b ea，那么xs2 = xs和xs t s = x对于所有的x ex, s, t ea *。这一事实适用于lrb型自动机和sl型自动机。我们的目的是确定所有S-act分别是右正则带型，左正则带型和半格型。为了达到这个目的，我们得到了对于任意给定集合X和任意半群S, X是S的充分必要条件，使得X分别是rrb型、lrb型和sl型(定理1、3、5)。进一步我们得到了更具体的结果，分别构造了rrb型、lrb型和sg型自动机(推论2、4、5)。设X是s行为。对于所有x E x，如果x S = x t，则用spt定义S上的关系p是众所周知的。得到X上的变换半群S/p。由此，由上述结果可以分别得到全变换半群T (X)中的每一个右正则带、左正则带和半带。
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Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0012
Do Long Van
{"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}
Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0003
K. Auinger
{"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}
Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0028
H. Nishio
{"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}
Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0005
V. Brattka
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.
{"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}
Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0034
M. Steinby
{"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}
Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0017
Isamu Inata
{"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}
Pub Date : 2003-07-01DOI: 10.1142/9789812704979_0033
K. Shum, M. Sen, Y. Guo
{"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}
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