{"title":"Randomized generation of error control codes with automata and transducers","authors":"S. Konstantinidis, Nelma Moreira, Rogério Reis","doi":"10.1051/ita/2018015","DOIUrl":"https://doi.org/10.1051/ita/2018015","url":null,"abstract":"We introduce the concept of an -maximal error-detecting block code, for some parameter in (0,1), in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our motivation for this is that it is computationally hard to decide whether an error-detecting block code is maximal. We present an output-polynomial time randomized algorithm that takes as input two positive integers N , l and a specification of the errors permitted in some application, and generates an error-detecting, or error-correcting, block code of length l that is 99%-maximal, or contains N words with a high likelihood. We model error specifications as (nondeterministic) transducers, which allow one to represent any rational combination of substitution and synchronization errors. We also present some elements of our implementation of various error-detecting properties and their associated methods. Then, we show several tests of the implemented randomized algorithm on various error specifications. A methodological contribution is the presentation of how various desirable error combinations can be expressed formally and processed algorithmically.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125944183","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 complexity of concatenation on deterministic and alternating finite automata","authors":"Michal Hospodár, Galina Jirásková","doi":"10.1051/ita/2018011","DOIUrl":"https://doi.org/10.1051/ita/2018011","url":null,"abstract":"We study the state complexity of the concatenation operation on regular languages represented by deterministic and alternating finite automata. For deterministic automata, we show that the upper bound m 2 n − k 2 n −1 on the state complexity of concatenation can be met by ternary languages, the first of which is accepted by an m -state DFA with k final states, and the second one by an n -state DFA with l final states for arbitrary integers m , n , k , l with 1 ≤ k ≤ m − 1 and 1 ≤ l ≤ n − 1. In the case of k ≤ m − 2, we are able to provide appropriate binary witnesses. In the case of k = m − 1 and l ≥ 2, we provide a lower bound which is smaller than the upper bound just by one. We use our binary witnesses for concatenation on deterministic automata to describe binary languages meeting the upper bound 2 m + n + 1 for the concatenation on alternating finite automata. This solves an open problem stated by Fellah et al. [ Int. J. Comput. Math. 35 (1990) 117–132].","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"235 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116433827","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":"Preface: Non-classical models of automata and applications VIII","authors":"Henning Bordihn, B. Nagy, György Vaszil","doi":"10.1051/ita/2018019","DOIUrl":"https://doi.org/10.1051/ita/2018019","url":null,"abstract":"Several non-classical models of automata and grammar-like structures are studied from different points of view in various areas of theoretical computer science, both as theoretical concepts and as formal models for applications. The purpose of the NCMA workshop series is to promote a deeper and interdisciplinary coverage of this particular area, and to foster new insights and substantial progress in computer science as a whole. The Eighth Workshop on Non-Classical Models of Automata and Applications (NCMA 2016) was organized by the Department of Computer Science of the Faculty of Informatics at the University of Debrecen, Hungary, August 29–30, 2016. The aim of the workshop was to provide an opportunity for researchers who work on different aspects of non-classical and classical models of automata and grammars to exchange and develop novel ideas.The history of the NCMA series goes back to 2009 when the first workshop on Non-Classical Models of Automata and Applications was held in Wroclaw, Poland, as a satellite event of the 17th International Sym-posium on Fundamentals of Computation Theory (FCT 2009). It was sponsored by the AutoMathA project of the European Science Foundation (ESF). The second workshop, NCMA 2010, was held in Jena, Germany, as an associated workshop of the 11th International Conference on Membrane Computing (CMC 11); the third workshop, NCMA 2011, was organized at the University of Milan, Italy, in close proximity to the 15th Conference on Developments in Language Theory (DLT 2011). After 2011, the NCMA workshops were organized as stand-alone events: NCMA 2012 in Fribourg, Switzerland, in August 2012; NCMA 2013 in Ume˚a, Sweden, in August 2013; NCMA 2014 in Kassel, Germany, in July 2014; and NCMA 2015 in Porto, Portugal, in August 31–September 1,","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133330432","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":"Automata with cyclic move operations for picture languages","authors":"F. Otto, F. Mráz","doi":"10.1051/ita/2018018","DOIUrl":"https://doi.org/10.1051/ita/2018018","url":null,"abstract":"Here, we study the cyclic extensions of Sgraffito automata and of deterministic two-dimensional two-way ordered restarting automata for picture languages. Such a cyclically extended automaton can move in a single step from the last column (or row) of a picture to the first column (or row). For Sgraffito automata, we show that this cyclic extension does not increase the expressive power of the model, while for deterministic two-dimensional two-way restarting automata, the expressive power is strictly increased by allowing cyclic moves. In fact, for the latter automata, we take the number of allowed cyclic moves in any column or row as a parameter, and we show that already with a single cyclic move per column (or row) the deterministic two-dimensional extended two-way restarting automaton can be simulated. On the other hand, we show that two cyclic moves per column or row already give the same expressive power as any finite number of cyclic moves.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131842157","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":"Parallel Computation on 2-3-Trees","authors":"W. Paul, U. Vishkin, H. Wagener","doi":"10.1051/ita/1983170403971","DOIUrl":"https://doi.org/10.1051/ita/1983170403971","url":null,"abstract":". — Our model of computation is a parallel computer with k synchronized processors P u ..., P k sharing a common random access storage, where simultaneous access to the same storage location by two or more processors is not allowed. Suppose a 2-3 tree Twith n leaves is implemented in the storage, suppose a u . .., a k are data that may or may not be stored in the leaves, suppose ö! ^ ... ^a k and for all i processor P t knows a t . We show how to search for a u . . ., a k in the tree T, how to insert these data into the tree and how to delete themfrom the tree in O {log n--log k) steps. Résumé. — Notre modèle de calcul est un ordinateur parallèle avec k processeurs synchronisés P u ..., Pk partageant une mémoire commune à accès aléatoire où un accès simultanément à la même adresse mémoire par deux processeurs ou plus est interdit. On suppose qu'un arbre 2-3 T à n feuilles est implanté dans la mémoire, que a u . .., a k sont des données qui peuvent être stockées dans les feuilles, on suppose que a^ ^ ... ^a k et que pour tout i, le processeur P t connaît a k On montre comment chercher a,, .. dans Varbre comment données Varbre et comment pas.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132133391","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 and powers of p∕q","authors":"J. Kari, Johan Kopra","doi":"10.1051/ITA/2017014","DOIUrl":"https://doi.org/10.1051/ITA/2017014","url":null,"abstract":"We consider one-dimensional cellular automata $F_{p,q}$ which multiply numbers by $p/q$ in base $pq$ for relatively prime integers $p$ and $q$. By studying the structure of traces with respect to $F_{p,q}$ we show that for $pgeq 2q-1$ (and then as a simple corollary for $p>q>1$) there are arbitrarily small finite unions of intervals which contain the fractional parts of the sequence $xi(p/q)^n$, ($n=0,1,2,dots$) for some $xi>0$. To the other direction, by studying the measure theoretical properties of $F_{p,q}$, we show that for $p>q>1$ there are finite unions of intervals approximating the unit interval arbitrarily well which don't contain the fractional parts of the whole sequence $xi(p/q)^n$ for any $xi>0$.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115410478","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":"Translation of a Digital Line into another according to various Digitization Processes","authors":"J. Borel","doi":"10.1051/ita/2017016","DOIUrl":"https://doi.org/10.1051/ita/2017016","url":null,"abstract":"We introduce unusual methods for the digitization process of a line. A square pixel of the computer screen is blackened when the line crosses a special part of this pixel, called the active pixel. The shape of this active pixel is discussed, in the following sense: can we obtain the new Freeman Code of the line, using of a mechanical transformation of the initial Freeman Code, which is the classical Cutting Sequence? Our choice is to limit mechanical transformations to the existence of a given transducer, so that everytime we put in (a power of) the classical Freeman Code of a line, the output recovers the new Freeman Code. Then we prove that such a transducer exists if and only if the active pixel is a polygon with rational vertices and big enough. The same result can be proved if we introduce several grey levels in the representation of the line. Then we get some antialising effects.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"91 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114066677","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":"A uniform cube-free morphism is k-power-free for all integers k ≥ 4","authors":"Francis Wlazinski","doi":"10.1051/ita/2017015","DOIUrl":"https://doi.org/10.1051/ita/2017015","url":null,"abstract":"In the study of k -power-free morphisms, the case of 3-free-morphisms, i.e. , cube-free morphisms, often differs from other k -power-free morphisms. Indeed, cube-freeness is less restrictive than square-freeness. And a cube provides less equations to solve than any integer k ≥ 4. Anyway, the fact that the image of a word by a morphism contains a cube implies relations that, under some assumptions, allow us to establish our main result: a cube-free uniform morphism is a k -power-free morphism for all integers k ≥ 4.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120959273","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":"Bipartite binomial heaps","authors":"Amr Elmasry, Claus Jensen, J. Katajainen","doi":"10.1051/ita/2017010","DOIUrl":"https://doi.org/10.1051/ita/2017010","url":null,"abstract":"We describe a heap data structure that supports Minimum, Insert, and Borrow at O (1) worst-case cost, Delete at O (lg n ) worst-case cost including at most lg n + O (1) element comparisons, and Union at O (lg n ) worst-case cost including at most lg n + O (lglg n ) element comparisons, where n denotes the (total) number of elements stored in the data structure(s) prior to the operation. As the resulting data structure consists of two components that are different variants of binomial heaps, we call it a bipartite binomial heap. Compared to its counterpart, a multipartite binomial heap, the new structure is simpler and mergeable, still retaining the efficiency of the other operations.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132782071","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":"Non-primitive words of the form pqm","authors":"Othman Echi","doi":"10.1051/ita/2017012","DOIUrl":"https://doi.org/10.1051/ita/2017012","url":null,"abstract":"Let p,q be two distinct primitive words. According to Lentin−Schutzenberger [], the language p + q + contains at most one non-primitive word and if p q m is not primitive, then . In this paper we give a sharper upper bound, namely, where ⌊ x ⌋ stands for the floor of x .","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125875292","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}