Limit sets of stable Cellular Automata

We study limit sets of stable cellular automata standing from a symbolic dynamics point of view where they are a special case of sofic shifts admitting a steady epimorphism. We prove that there exists a right-closing almost-everywhere steady factor map from one irreducible sofic shift onto another one if and only if there exists such a map from the domain onto the minimal right-resolving cover of the image. We define right-continuing almost-everywhere steady maps and prove that there exists such a steady map between two sofic shifts if and only if there exists a factor map from the domain onto the minimal right-resolving cover of the image. In terms of cellular automata, this translates into: A sofic shift can be the limit set of a stable cellular automaton with a right-closing almost-everywhere dynamics onto its limit set if and only if it is the factor of a fullshift and there exists a right- closing almost-everywhere factor map from the sofic shift onto its minimal right- resolving cover. A sofic shift can be the limit set of a stable cellular automaton reaching its limit set with a right-continuing almost-everywhere factor map if and only if it is the factor of a fullshift and there exists a factor map from the sofic shift onto its minimal right-resolving cover. Finally, as a consequence of the previous results, we provide a characterization of the Almost of Finite Type shifts (AFT) in terms of a property of steady maps that have them as range.Comment: 18 pages, 3 figure

Structural aspects of tilings

In this paper, we study the structure of the set of tilings produced by any given tile-set. For better understanding this structure, we address the set of finite patterns that each tiling contains. This set of patterns can be analyzed in two different contexts: the first one is combinatorial and the other topological. These two approaches have independent merits and, once combined, provide somehow surprising results. The particular case where the set of produced tilings is countable is deeply investigated while we prove that the uncountable case may have a completely different structure. We introduce a pattern preorder and also make use of Cantor-Bendixson rank. Our first main result is that a tile-set that produces only periodic tilings produces only a finite number of them. Our second main result exhibits a tiling with exactly one vector of periodicity in the countable case.Comment: 11 page

The domino problem on groups of polynomial growth

We characterize the virtually nilpotent finitely generated groups (or, equivalently by Gromov's theorem, groups of polynomial growth) for which the Domino Problem is decidable: These are the virtually free groups, i.e. finite groups, and those having $\Z$ as a subgroup of finite index

Classification d’apprenants francophones de l’anglais sur la base des métriques de complexité lexicale et syntaxique

International audienceThis paper assesses spontaneous oral monologues in the ANGLISH corpus (Tortel 2009). Twenty oral transcriptions of NS English are compared with forty French-L1 transcriptions of NNS English of intermediate and advanced levels. Syntactic and complexity metrics (Lu 2014) and Vocabulary Growth Curves (Evert & Baroni 2008, Baayen 2008) are used to classify speakers. We analyse how significant these written-based metrics are in the classification of speakers for their oral production.Cette contribution examine les monologues en oral spontané du corpus ANGLISH (Tortel 2009). Les productions orales de vingt locuteurs natifs sont comparées aux monologues produits par les quarante locuteurs francophones de niveau intermédiaire et avancé. Les métriques de complexité syntaxique et lexicale implémentées dans des analyseurs (Lu 2014) sont utilisées pour essayer de classer les locuteurs. Enfin, à partir des courbes de croissance du vocabulaire et des modèles LNRE (Baayen 2008), on cherche à évaluer la pertinence de ces métriques de l’écrit pour la classification des locuteurs en fonction de leur production orale

Tilings and model theory

ISBN 978-5-94057-377-7International audienceIn this paper we emphasize the links between model theory and tilings. More precisely, after giving the definitions of what tilings are, we give a natural way to have an interpretation of the tiling rules in first order logics. This opens the way to map some model theoretical properties onto some properties of sets of tilings, or tilings themselves

Modélisation de l’intonation interlangue: le cas des questions

International audienceIn this paper, we study the intonational patterns observed in learners’ productions in order to evaluate what motivates the deviations observed: systemic differences between the learners’ L1 and the L2, differences in phonetic implementation, etc. The analysis consists of a cross-comparison of the intonation of yes-no questions in French, English and English as an L2. It is based on five information-seeking yes no questions that were extracted from the AixOx corpus, which contains a set of 40 texts that were read by 10 native French speakers, 10 Native English speakers and 20 French learners of English. The analysis of the data showed that the differences between native and non-native speakers do not affect the form of the nuclear contour. It mostly shows that French speakers of English have a tendency to assign a rising pitch movement at the end of prosodic words, which leads to a clear difference in rhythm.Cet article propose d’étudier les patrons prosodiques observés dans la production d’apprenants afin d’évaluer ce qui contraint les déviances : des différences systémiques entre la L1 des apprenants et la L2, des différences d’implémentation phonétique, etc. L’analyse consiste en une étude croisée de l’intonation des questions polaires en français, en anglais et en anglais L2. Cinq questions polaires ont été extraites du corpus AixOx, ensemble de 40 textes qui ont été lus par 10 locuteurs natifs de français, 10 locuteurs natifs d’anglais et 20 apprenants francophones d’anglais (10 de niveau indépendant et 10 de niveau expérimenté). L’analyse des données montre que les différences entre natifs et non natifs n’affectent pas la forme du contour nucléaire, mais que les apprenants francophones d’anglais tendent à assigner un mouvement montant à la fin des mots prosodiques, ce qui engendre une claire différence de rythme

On Derivatives and Subpattern Orders of Countable Subshifts

We study the computational and structural aspects of countable two-dimensional SFTs and other subshifts. Our main focus is on the topological derivatives and subpattern posets of these objects, and our main results are constructions of two-dimensional countable subshifts with interesting properties. We present an SFT whose iterated derivatives are maximally complex from the computational point of view, a sofic shift whose subpattern poset contains an infinite descending chain, a family of SFTs whose finite subpattern posets contain arbitrary finite posets, and a natural example of an SFT with infinite Cantor-Bendixon rank.Comment: In Proceedings AUTOMATA&JAC 2012, arXiv:1208.249

Turing degrees of limit sets of cellular automata

Cellular automata are discrete dynamical systems and a model of computation. The limit set of a cellular automaton consists of the configurations having an infinite sequence of preimages. It is well known that these always contain a computable point and that any non-trivial property on them is undecidable. We go one step further in this article by giving a full characterization of the sets of Turing degrees of cellular automata: they are the same as the sets of Turing degrees of effectively closed sets containing a computable point

Investigating Acoustic Correlates of Whisper Scoring for L2 Speech Using Forced alignment with the Italian Component of the ISLE corpus

This paper analyses how global phonetic analyses of learner data can be used to confirm Whisper probability scores assigned to learner phonetic data. We explore the Italian component of the ISLE corpus with phonetic analyses of 23 learners of English. Using a C++ wrapper of the Whisper models, we investigate the probability scores assigned by Whisper's tiny model. We discuss the phonetic features that may account for these Whisper predictions using P2FA-forced alignment. We try to correlate the quality of the phonetic realisation (measured using Levenshtein distance to the read text) to global vocalic measurements such as the convex hull or Euclidian distances between monophthongs. We show that Levenshtein distance to the reference transcription of the Whisper tidy model correlates with the grades assigned by the annotators and partially to the accuracy of the classification of monophthongs using the k-NN algorithm