L-Convex Polyominoes are Recognizable in Real Time by 2D Cellular Automata

A polyomino is said to be L-convex if any two of its cells are connected by a 4-connected inner path that changes direction at most once. The 2-dimensional language representing such polyominoes has been recently proved to be recognizable by tiling systems by S. Brocchi, A. Frosini, R. Pinzani and S. Rinaldi. In an attempt to compare recognition power of tiling systems and cellular automata, we have proved that this language can be recognized by 2-dimensional cellular automata working on the von Neumann neighborhood in real time. Although the construction uses a characterization of L-convex polyominoes that is similar to the one used for tiling systems, the real time constraint which has no equivalent in terms of tilings requires the use of techniques that are specific to cellular automata

Efficient universal pushdown cellular automata and their application to complexity

In order to obtain universal classical cellular automata an infinite space is required. Therefore, the number of required processors depends on the length of input data and, additionally, may increase during the computation. On the other hand, Turing machines are universal devices which have one processor only and additionally an infinite storage tape. Here an in some sense intermediate model is studied. The pushdown cellular automata are a stack augmented generalization of classical cellular automata. They form a massively parallel universal model where the number of processors is bounded by the length of input data. Effcient universal pushdown cellular automata and their efficiently verifiable encodings are proposed. They are applied to computational complexity, and tight time and stack-space hierarchies are shown. CR Subject Classification (1998): F.1, F.4.3, B.6.1, E.

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

Sanakielet ja lokaalisuus

In this master's thesis we study the generalization of word languages into multi-dimensional arrays of letters i.e picture languages. Our main interest is the class of recognizable picture languages which has many properties in common with the robust class of regular word languages. After surveying the basic properties of picture languages, we present a logical characterization of recognizable picture languages—a generalization of Büchi's theorem of word languages into pictures, namely that the class of recognizable picture languages is the one recognized by existential monadic second-order logic. The proof presented is a recent one that makes the relation between tilings and logic clear in the proof. By way of the proof we also study the locality of the model theory of picture structures through logical locality obtained by normalization of EMSO on those structures. A continuing theme in the work is also to compare automata and recognizability between word and picture languages. In the fourth section we briefly look at topics related to computativity and computational complexity of recognizable picture languages

Descriptive complexity for pictures languages

This paper deals with logical characterizations of picture languages of any dimension by syntactical fragments of existential second-order logic. Two classical classes of picture languages are studied: - the class of "recognizable" picture languages, i.e. projections of languages defined by local constraints (or tilings): it is known as the most robust class extending the class of regular languages to any dimension; - the class of picture languages recognized on "nondeterministic cellular automata in linear time" : cellular automata are the simplest and most natural model of parallel computation and linear time is the minimal time-bounded class allowing synchronization of nondeterministic cellular automata. We uniformly generalize to any dimension the characterization by Giammarresi et al. (1996) of the class of "recognizable" picture languages in existential monadic second-order logic. We state several logical characterizations of the class of picture languages recognized in linear time on nondeterministic cellular automata. They are the first machine-independent characterizations of complexity classes of cellular automata. Our characterizations are essentially deduced from normalization results we prove for first-order and existential second-order logics over pictures. They are obtained in a general and uniform framework that allows to extend them to other "regular" structures

Complex Systems: A Survey

A complex system is a system composed of many interacting parts, often called agents, which displays collective behavior that does not follow trivially from the behaviors of the individual parts. Examples include condensed matter systems, ecosystems, stock markets and economies, biological evolution, and indeed the whole of human society. Substantial progress has been made in the quantitative understanding of complex systems, particularly since the 1980s, using a combination of basic theory, much of it derived from physics, and computer simulation. The subject is a broad one, drawing on techniques and ideas from a wide range of areas. Here I give a survey of the main themes and methods of complex systems science and an annotated bibliography of resources, ranging from classic papers to recent books and reviews.Comment: 10 page