{"title":"Tree algebra of sofic tree languages","authors":"N. Aubrun, Marie-Pierre Béal","doi":"10.1051/ita/2014018","DOIUrl":"https://doi.org/10.1051/ita/2014018","url":null,"abstract":"We consider the languages of finite trees called tree-shift languages which are factorial extensible tree languages. These languages are sets of factors of subshifts of infinite trees. We give effective syntactic characterizations of two classes of regular tree-shift languages: the finite type tree languages and the tree languages which are almost of finite type. Each class corresponds to a class of subshifts of trees which is invariant by conjugacy. For this goal, we define a tree algebra which is finer than the classical syntactic tree algebra based on contexts. This allows us to capture the notion of constant tree which is essential in the framework of tree-shift languages.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"486 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129796012","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":"Existence of an infinite ternary 64-abelian square-free word","authors":"M. Huova","doi":"10.1051/ita/2014012","DOIUrl":"https://doi.org/10.1051/ita/2014012","url":null,"abstract":"We consider a recently defined notion of k -abelian equivalence of words by\u0000 concentrating on avoidance problems. The equivalence class of a word depends on the\u0000 numbers of occurrences of different factors of length k for a fixed natural\u0000 number k and\u0000 the prefix of the word. We have shown earlier that over a ternary alphabet k -abelian squares cannot be\u0000 avoided in pure morphic words for any natural number k . Nevertheless,\u0000 computational experiments support the conjecture that even 3-abelian squares can be\u0000 avoided over ternary alphabets. In this paper we establish the first avoidance result\u0000 showing that by choosing k to be large enough we have an infinite\u0000 k -abelian\u0000 square-free word over three letter alphabet. In addition, this word can be obtained as a\u0000 morphic image of a pure morphic word.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"152 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134031002","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":"Abelian pattern avoidance in partial words","authors":"F. Blanchet-Sadri, B. Winkle, S. Simmons","doi":"10.1051/ita/2014014","DOIUrl":"https://doi.org/10.1051/ita/2014014","url":null,"abstract":"Pattern avoidance is an important topic in combinatorics on words which dates back to the beginning of the twentieth century when Thue constructed an infinite word over a ternary alphabet that avoids squares, i.e. , a word with no two adjacent identical factors. This result finds applications in various algebraic contexts where more general patterns than squares are considered. On the other hand, Erdős raised the question as to whether there exists an infinite word that avoids abelian squares, i.e. , a word with no two adjacent factors being permutations of one another. Although this question was answered affirmately years later, knowledge of abelian pattern avoidance is rather limited. Recently, (abelian) pattern avoidance was initiated in the more general framework of partial words, which allow for undefined positions called holes. In this paper, we show that any pattern p with n > 3 distinct variables of length at least 2 n is abelian avoidable by a partial word with infinitely many holes, the bound on the length of p being tight. We complete the classification of all the binary and ternary patterns with respect to non-trivial abelian avoidability, in which no variable can be substituted by only one hole. We also investigate the abelian avoidability indices of the binary and ternary patterns.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132730862","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}
R. Jungers, V. Bruyère, Romain Hollanders, M. Rigo
{"title":"Special issue in the honor of the 14th \"Journées Montoises d'Informatique Théorique\" - Foreword","authors":"R. Jungers, V. Bruyère, Romain Hollanders, M. Rigo","doi":"10.1051/ita/2014011","DOIUrl":"https://doi.org/10.1051/ita/2014011","url":null,"abstract":"It is our pleasure to release this special issue in the honor of the “fourteenth Journees Montoises d’Informatique Theorique” which were held at the Universite catholique de Louvain, Belgium, in September 2012. The conference welcomed more than 80 participants, and about forty speakers from several countries such as Belgium, Canada, Czech Republic, Finland, France, Germany, Italy, Marocco, Russia, UK, US, . . . In particular, we were honored to hear plenary talks by Profs. Marie-Pierre Beal, Jean Cardinal, Maxime Crochemore, Fabien Durand, Julien Hendrickx, Juhani Karhumaki, and Mikhail Volkov. We have selected twelve papers for this special issue. Each paper has been refereed by at least two independent reviewers. The papers reflect well the rich and various topics of the conference which explore the main challenges in formal language and automata theory and its connections with discrete mathematics and theoretical computer science among which numeration systems and Rauzy fractals, combinatorics on words, repetitions in words and pattern avoidance, morphic words, symbolic dynamics, tree languages, enumeration and asymptotic growth of languages, . . . We wish to heartily thank Isabelle Hisette, Prof. Ph. Lefevre, the F.R.S.-FNRS, and the University for their help and support. Also, this Issue would not have been possible without the help of the many referees. Let them all be thanked for their precious and very serious work. We finally thank Prof. Ch. Choffrut and the editorial staff of RAIRO-TIA for allowing us to publish this special issue.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"169 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114839365","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":"Root clustering of words","authors":"G. Lischke","doi":"10.1051/ita/2014009","DOIUrl":"https://doi.org/10.1051/ita/2014009","url":null,"abstract":"Six kinds of both of primitivity and periodicity of words, introduced by Ito and Lischke\u0000 [M. Ito and G. Lischke, Math. Log. Quart. 53 (2007) 91–106;\u0000 Corrigendum in Math. Log. Quart. 53 (2007) 642–643], give\u0000 rise to defining six kinds of roots of a nonempty word. For 1 ≤ k ≤ 6, a\u0000 k -root word\u0000 is a word which has exactly k different roots, and a k -cluster is a set of\u0000 k -root\u0000 words u where\u0000 the roots of u fulfil a given prefix relationship. We show that\u0000 out of the 89 different clusters that can be considered at all, in fact only 30 exist, and\u0000 we give their quasi-lexicographically smallest elements. Also we give a sufficient\u0000 condition for words to belong to the only existing 6-cluster. These words are also called\u0000 Lohmann words. Further we show that, with the exception of a single cluster, each of the\u0000 existing clusters contains either only periodic words, or only primitive words.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133589691","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}
Florian Horn, W. Thomas, N. Wallmeier, Martin Zimmermann
{"title":"Optimal strategy synthesis for request-response games","authors":"Florian Horn, W. Thomas, N. Wallmeier, Martin Zimmermann","doi":"10.1051/ita/2015005","DOIUrl":"https://doi.org/10.1051/ita/2015005","url":null,"abstract":"We show the existence and effective computability of optimal (even finite-state) winning strategies for request-response games in case the quality of a play is measured by the limit superior of the mean accumulated waiting times between requests and their responses.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128967255","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":"One-Rule Length-Preserving Rewrite Systems and Rational Transductions","authors":"M. Latteux, Yves Roos","doi":"10.1051/ita/2013044","DOIUrl":"https://doi.org/10.1051/ita/2013044","url":null,"abstract":"We address the problem to know whether the relation induced by a one-rule length-preserving rewrite system is rational. We partially answer to a conjecture of Eric Lilin who conjectured in 1991 that a one-rule length-preserving rewrite system is a rational transduction if and only if the left-hand side u and the right-hand side v of the rule of the system are not quasi-conjugate or are equal, that means if u and v are distinct, there do not exist words x , y and z such that u = xyz and v = zyx . We prove the only if part of this conjecture and identify two non trivial cases where the if part is satisfied.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114255268","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 Generalized Model of PAC Learning and its Applicability","authors":"Thomas Brodag, S. Herbold, S. Waack","doi":"10.1051/ita/2014005","DOIUrl":"https://doi.org/10.1051/ita/2014005","url":null,"abstract":"We combine a new data model, where the random classification is subjected to rather weak restrictions which in turn are based on the Mammen−Tsybakov [E. Mammen and A.B. Tsybakov, Ann. Statis. 27 (1999) 1808–1829; A.B. Tsybakov, Ann. Statis. 32 (2004) 135–166.] small margin conditions, and the statistical query (SQ) model due to Kearns [M.J. Kearns, J. ACM 45 (1998) 983–1006] to what we refer to as PAC + SQ model. We generalize the class conditional constant noise (CCCN) model introduced by Decatur [S.E. Decatur, in ICML ’97: Proc. of the Fourteenth Int. Conf. on Machine Learn. Morgan Kaufmann Publishers Inc. San Francisco, CA, USA (1997) 83–91] to the noise model orthogonal to a set of query functions. We show that every polynomial time PAC + SQ learning algorithm can be efficiently simulated provided that the random noise rate is orthogonal to the query functions used by the algorithm given the target concept. Furthermore, we extend the constant-partition classification noise (CPCN) model due to Decatur [S.E. Decatur, in ICML ’97: Proc. of the Fourteenth Int. Conf. on Machine Learn. Morgan Kaufmann Publishers Inc. San Francisco, CA, USA (1997) 83–91] to what we call the constant-partition piecewise orthogonal (CPPO) noise model. We show how statistical queries can be simulated in the CPPO scenario, given the partition is known to the learner. We show how to practically use PAC + SQ simulators in the noise model orthogonal to the query space by presenting two examples from bioinformatics and software engineering. This way, we demonstrate that our new noise model is realistic.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114015450","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":"Computing Depths of Patterns","authors":"F. Blanchet-Sadri, A. Lohr","doi":"10.1051/ita/2016014","DOIUrl":"https://doi.org/10.1051/ita/2016014","url":null,"abstract":"Pattern avoidance is an important research topic in combinatorics on words which dates back to Thue's construction of an infinite word over three letters that avoids squares, i.e., a sequence with no two adjacent identical factors. This result finds applications in various algebraic contexts where more general patterns than squares are considered. A more general form of pattern avoidance has recently emerged to allow for undefined positions in sequences. New concepts on patterns such as depth have been introduced and a number of questions have been raised, some of them we answer. In the process, we prove a strict bound on the number of square occurrences in an unavoidable pattern, and consequently, any pattern with more square occurrences than distinct variables is avoidable over three letters. We also prove a strict bound on the length of an avoidable pattern with at least four distinct variables. We finally provide an algorithm that determines whether a given pattern is of bounded depth, and if so, computes its depth.","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128784920","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":"One quantifier alternation in first-order logic with modular predicates","authors":"Manfred Kufleitner, Tobias Walter","doi":"10.1051/ita/2014024","DOIUrl":"https://doi.org/10.1051/ita/2014024","url":null,"abstract":"Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison $x<y$ and predicates for $x equiv i mod n$ has been investigated by Barrington, Compton, Straubing and Therien. The study of FO[<,MOD]-fragments was initiated by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that definability in the two-variable fragment FO2[<,MOD] is decidable. In this paper we continue this line of work. We give an effective algebraic characterization of the word languages in Sigma2[<,MOD]. The fragment Sigma2 consists of first-order formulas in prenex normal form with two blocks of quantifiers starting with an existential block. In addition we show that Delta2[<,MOD], the largest subclass of Sigma2[<,MOD] which is closed under negation, has the same expressive power as two-variable logic FO2[<,MOD]. This generalizes the result FO2[<] = Delta2[<] of Therien and Wilke to modular predicates. As a byproduct, we obtain another decidable characterization of FO2[<,MOD].","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"64 4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130765843","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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