{"title":"Words, Dyck Paths, Trees, and Bijections","authors":"H. Prodinger","doi":"10.1142/9789812810908_0028","DOIUrl":"https://doi.org/10.1142/9789812810908_0028","url":null,"abstract":"In cite{BaDeFePi96} the concept of nondecreasing Dyck paths was introduced. We continue this research by looking at it from the point of view of words, rational languages, planted plane trees, and continued fractions. \u0000We construct a bijection with planted plane trees of height $le 4$ and compute various statistics on trees that are the equivalents of nondecreasing Dyck paths.","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123713931","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":"Some Operators on Families of Fuzzy Languages and Their Monoids","authors":"P. Asveld","doi":"10.1142/9789812810908_0001","DOIUrl":"https://doi.org/10.1142/9789812810908_0001","url":null,"abstract":"We study the structure of partially ordered monoids generated by certain operators on families of fuzzy languages. These operators are induced by simple, well-known operations on fuzzy languages, like fuzzy homomorphism, fuzzy finite substitution and intersection with regular fuzzy languages. The structure of these monoids provides better insight in the (in)dependency of closure properties of some families of fuzzy languages.","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124328547","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 Isomorphic Representations of Monotone Tree and Nondeterministic Tree","authors":"F. Gécseg, B. Imreh","doi":"10.1142/9789812810908_0011","DOIUrl":"https://doi.org/10.1142/9789812810908_0011","url":null,"abstract":"","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129408446","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":"Iterated Morphisms with Complementarity on the DNA Alphabet","authors":"A. Salomaa","doi":"10.1142/9789812810908_0031","DOIUrl":"https://doi.org/10.1142/9789812810908_0031","url":null,"abstract":"Watson-Crick complementarity can be viewed as a language-theoretic operation: \"bad\" words obtained through a generative process are replaced by their complementary ones. This idea seems particularly suitable for Linden- mayer systems. D0L systems augmented with a specific complementarity transition, Watson-Crick D0L systems, have turned out to be a most interesting model and have already been extensively studied. In the present paper, attention is focused on Watson-Crick D0L systems, where the alphabet is the original four-letter DNA alphabet {A, G, T , C}. Growth functions and various decision problems will be investigated. Previously known cases about growth functions that are not Z-rational deal with alphabets bigger than the DNA alphabet, and it has been an open problem whether similar constructions can be carried out for the DNA alphabet. The main result in this paper shows that this is indeed the case.","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"454 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2001-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122938893","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 Sparse 0L Languages Over the Binary Alphabet","authors":"J. Honkala","doi":"10.1142/9789812810908_0014","DOIUrl":"https://doi.org/10.1142/9789812810908_0014","url":null,"abstract":"Latteux and Thierrin have characterized sparse context-free languages by showing that a context-free language L is sparse if and only if L is bound- ed. We prove a similar result for binary 0L languages which are not D0L languages.","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2000-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121652258","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":"Visualizing Languages Using Primitive Powers","authors":"T. Head","doi":"10.1142/9789812810908_0013","DOIUrl":"https://doi.org/10.1142/9789812810908_0013","url":null,"abstract":"","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"82 3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131507961","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":"Minimal Recognizers and Syntactic Monoids of DR Tree Languages","authors":"F. Gécseg, M. Steinby","doi":"10.1142/9789812810908_0012","DOIUrl":"https://doi.org/10.1142/9789812810908_0012","url":null,"abstract":"","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"67 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132995823","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":"Liars, Demons, and Chaos","authors":"Cristian S. Calude, E. Calude, P. Kay","doi":"10.1142/9789812810908_0003","DOIUrl":"https://doi.org/10.1142/9789812810908_0003","url":null,"abstract":"","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"313 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122984747","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":"String Operations Suggested by DNA Biochemistry: The Balanced Cut Operation","authors":"L. Kari, A. Paun","doi":"10.1142/9789812810908_0021","DOIUrl":"https://doi.org/10.1142/9789812810908_0021","url":null,"abstract":"We introduce and investigate an operation with strings suggested by DNA processing (by means of exonucleases): the operation of cutting strings of equal length from the beginning and the end of a string. A related operation is that of cutting a square of a string from the preex of a string. The closure properties of families in the Chomsky hierarchy are investigated (and, with one exception, for the case of linear languages, settled).","PeriodicalId":439470,"journal":{"name":"Words, Semigroups, and Transductions","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133354919","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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