Characterizations of recognizable picture series

AbstractThe theory of two-dimensional languages as a generalization of formal string languages was motivated by problems arising from image processing and pattern recognition, and also concerns models of parallel computing. Here we investigate power series on pictures. These are functions that map pictures to elements of a semiring and provide an extension of two-dimensional languages to a quantitative setting. We assign weights to different devices, ranging from picture automata to tiling systems. We will prove that, for commutative semirings, the behaviours of weighted picture automata are precisely alphabetic projections of series defined in terms of rational operations, and also coincide with the families of series characterized by weighted tiling or weighted domino systems

The Height of Piecewise-Testable Languages with Applications in Logical Complexity

The height of a piecewise-testable language L is the maximum length of the words needed to define L by excluding and requiring given subwords. The height of L is an important descriptive complexity measure that has not yet been investigated in a systematic way. This paper develops a series of new techniques for bounding the height of finite languages and of languages obtained by taking closures by subwords, superwords and related operations. As an application of these results, we show that FO^2(A^*, subword), the two-variable fragment of the first-order logic of sequences with the subword ordering, can only express piecewise-testable properties and has elementary complexity

Deterministic recognizability of picture languages with Wang automata

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to ApplicationsInternational audienceWe present a model of automaton for picture language recognition, called Wang automaton, which is based on labeled Wang tiles. Wang automata combine features of both online tessellation acceptors and 4-way automata: as in online tessellation acceptors, computation assigns states to each picture position; as in 4-way automata, the input head visits the picture moving from one pixel to an adjacent one, according to some scanning strategy. Wang automata recognize the class REC, i.e. they are equivalent to tiling systems or online tessellation acceptors, and hence strictly more powerful than 4-way automata. We also introduce a natural notion of determinism for Wang automata, and study the resulting class, extending the more traditional approach of diagonal-based determinism, used e. g. by deterministic tiling systems. In particular, we prove that the concept of row (or column) ambiguity defines the class of languages recognized by Wang automata directed by boustrophedonic scanning strategies

Workshop on Formal Languages, Automata and Petri Nets

This report contains abstracts of the lectures presented at the workshop 'Formal Languages, Automata and Petri-Nets' held at the University of Stuttgart on January 16-17, 1998. The workshop brought together partners of the German-Hungarian project No. 233.6, Forschungszentrum Karlsruhe, Germany, and No. D/102, TeT Foundation, Budapest, Hungary. It provided an opportunity to present work supported by this project as well as related topics

Logic and Automata

Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field

Proceedings of JAC 2010. Journées Automates Cellulaires

The second Symposium on Cellular Automata “Journ´ees Automates Cellulaires” (JAC 2010) took place in Turku, Finland, on December 15-17, 2010. The first two conference days were held in the Educarium building of the University of Turku, while the talks of the third day were given onboard passenger ferry boats in the beautiful Turku archipelago, along the route Turku–Mariehamn–Turku. The conference was organized by FUNDIM, the Fundamentals of Computing and Discrete Mathematics research center at the mathematics department of the University of Turku. The program of the conference included 17 submitted papers that were selected by the international program committee, based on three peer reviews of each paper. These papers form the core of these proceedings. I want to thank the members of the program committee and the external referees for the excellent work that have done in choosing the papers to be presented in the conference. In addition to the submitted papers, the program of JAC 2010 included four distinguished invited speakers: Michel Coornaert (Universit´e de Strasbourg, France), Bruno Durand (Universit´e de Provence, Marseille, France), Dora Giammarresi (Universit` a di Roma Tor Vergata, Italy) and Martin Kutrib (Universit¨at Gie_en, Germany). I sincerely thank the invited speakers for accepting our invitation to come and give a plenary talk in the conference. The invited talk by Bruno Durand was eventually given by his co-author Alexander Shen, and I thank him for accepting to make the presentation with a short notice. Abstracts or extended abstracts of the invited presentations appear in the first part of this volume. The program also included several informal presentations describing very recent developments and ongoing research projects. I wish to thank all the speakers for their contribution to the success of the symposium. I also would like to thank the sponsors and our collaborators: the Finnish Academy of Science and Letters, the French National Research Agency project EMC (ANR-09-BLAN-0164), Turku Centre for Computer Science, the University of Turku, and Centro Hotel. Finally, I sincerely thank the members of the local organizing committee for making the conference possible. These proceedings are published both in an electronic format and in print. The electronic proceedings are available on the electronic repository HAL, managed by several French research agencies. The printed version is published in the general publications series of TUCS, Turku Centre for Computer Science. We thank both HAL and TUCS for accepting to publish the proceedings.Siirretty Doriast

Subshifts with sparse traces

We study two-dimensional subshifts whose horizontal trace (also called projective subdynamics) contains only configurations of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As corollaries, we obtain new proofs for various known results on traces of SFTs, nilpotency, and decidability results for cellular automata and topological full groups. We also construct various (sofic) examples illustrating the concepts

On Piecewise Testable, Starfree, and Recognizable Picture Languages

. We isolate a technique for showing that a picture language (i.e. a "two-dimensional language") is not recognizable. Then we prove the non-recognizability of a picture language that is both starfree (i.e., definable by means of union, concatenation, and complement) and piecewise testable (i.e., definable by means of allowed subpictures), solving an open question in [GR96]. We also define local, locally testable, and locally threshold testable picture languages and summarize known inclusion results for these classes. The classes of piecewise testable, locally testable, and locally threshold testable picture languages can, as in the word case, be characterized by certain (fragments of) first-order logics. 1 Introduction In [GRST96,GR96], the authors investigated the class of recognizable picture language (as a straightforward generalization of recognizable word languages to two dimensions), and compared it to variants of classes of regular picture languages, defined by "regular express..