Deterministically and Sudoku-Deterministically Recognizable Picture Languages

The recognizable 2-dimensional languages are a robust class with many characterizations, comparable to the regular languages in the 1-dimensional case. One characterization is by tiling systems. The corresponding word problem is NP-complete. Therefore, notions of determinism for tiling systems were suggested. For the notion which was called "deterministically recognizable" it was open since 1998 whether it implies recognizability. By showing that acyclicity of grid graphs is recognizable we answer this question positively. In contrast to that, we show that non-recognizable languages can be accepted by a generalization of this tiling system determinism which we call sudoku-determinism. Its word problem, however, is still in linear time. We show that Sudoku-determinism even contains the set of 2-dimensional languages which can be recognized by 4-way alternating automata

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

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

Perfectly quilted rectangular snake tilings

AbstractWe introduce a particular form of snake tilings to define picture languages, and relate the obtained family to the recognizable picture languages (as defined by Wang tiles). The correspondence for substitution tilings is even closer, and hence is applicable to the Hilbert curve

Picture languages generated by splicing and assembling til·les

Idiomes imatge generats per Empalme i Muntatge Rajoles. L'extensió de l'estudi de les llengües oficials sobre el cas string 2 idiomes dimensionals o idiomes imatge ha estat d'interès per molt temps per les seves vastes aplicacions. En la tesi i l'objecte de dues dimensions més comú estudiat és una imatge que és una matriu rectangular de símbols presos a partir d'un alfabet finit. L 'objectiu d'aquesta tesi se centra en l'estudi de la generació de les classes d'idiomes d'imatge per les operacions de bio-inspirats saber, `Enllaç' i` Auto-Assemblea 'd'ADN-Computing. És a dir, sistema d'entroncament i enrajolats Regla Sistemes H-Array. H-array Empalme Sistema és un formalisme bio-inspirat estès des H-entroncament de la caixa de cadena, un estudi àmpliament investigat introduït per T. Head. Està estructurat com un mecanisme mitjançant l'estudi de les gramàtiques lineals de dues dimensions correctes. Aquest formalisme és un mecanisme que s'aplica al número finit d'imatges trucades imatges inicials amb determinat conjunt de regles d'entroncament de dòmino de columna i fila. El lloc de context en el qual les dues imatges es tallen en columnes i files es va decidir per la seqüència de dòmino adjacents en el conjunt de regles. I llavors el `enganxar 'de la primera part de la imatge a la segona part de la imatge es realitza mitjançant la columna i fila concatenacions respectivament. L'H-Array Enllaç Sistemes s'aplica sobre llengües 2D-RLG generant idiomes Enllaç H-Array (HASL). A continuació, les classes de restricció definides i d'estudi són acte Creu sobre matrius i llenguatges Empalme matriu simples i resultats incomparables es va demostrar amb 2D-RLG, HASL. No són disjunts i es creuen llenguatges recognoscibles. El segon formalisme principal introduït i estudiat a la tesi és Revestiments Sistema de regles . Aquest formalisme genera la imatge pel conjunt de regles de mosaic, muntatge rajoles. Hem demostrat que la classe de L (TS) (Sistema d'enrajolat, llenguatge reconeixible) està continguda en TRuS. A més, vam demostrar existeixen una construcció del formalisme basat en la generació d'imatges en files o columnes que és equivalent a L (TS). L'equivalència es demostra l'ús de sistemes de Wang. Així que porta a una idea interessant d funcionament bio-inspirat (auto-acoblament) a la generació de la imatge.Idiomas de imagen generados por Empalme y Montaje Azulejos. La extensión del estudio de las lenguas oficiales sobre el caso string dos idiomas dimensionales o idiomas imagen ha sido de interés por mucho tiempo por sus vastas aplicaciones. En la tesis y el objeto de dos dimensiones más común estudiado es una imagen que es una matriz rectangular de símbolos tomados a partir de un alfabeto finito. E l objetivo de esta tesis se centra en el estudio de la generación de las clases de idiomas de imagen por las operaciones de bio-inspirados saber, `Empalme 'y` Auto-Asamblea' de ADN-Computing. A saber, sistema de empalme H-Array y sistemas de regla de mosaico. H-array Empalme Sistema es un formalismo bio-inspirado extendido desde H-empalme de la caja de cadena, un estudio ampliamente investigado introducido por T. Head. Está estructurado como un mecanismo mediante el estudio de las gramáticas lineales de dos dimensiones correctas. Este formalismo es un mecanismo que se aplica en el número finito de imágenes llamadas imágenes iniciales con determinado conjunto de reglas de empalme de dominó de columna y fila. El sitio de contexto en el que las dos imágenes se cortan en columnas y filas se decidió por la secuencia de dominós adyacentes en el conjunto de reglas. Y entonces el `pegar 'de la primera parte (o sub-array) de la imagen a la segunda parte de la imagen se realiza mediante la columna y fila concatenaciones respectivamente. El H-Array Empalme Sistemas se aplica sobre lenguas 2D-RLG generando idiomas Empalme H-Array (HASL). A continuación, las clases de restricciones definidas y de estudio son auto Cruz sobre matrices y lenguajes Empalme matriz simples y resultados incomparables se demostró con 2D-RLG, HASL. No son disjuntos y se cruzan lenguajes reconocibles. El segundo formalismo principal introducido y estudiado en la tesis son Revestimientos Sistema de reglas TRuS. Este formalismo genera la imagen por el conjunto de reglas de mosaico, montajes azulejos. Hemos demostrado que la clase de L (TS) (Sistema de alicatado, lenguaje reconocible) está contenida en la TRuS. Además, demostramos existen una construcción del formalismo basado en la generación de imágenes en filas o columnas que es equivalente a L (TS). La equivalencia se demuestra el uso de sistemas de Wang.Picture languages generated by Splicing and Assembling Tiles. The extension of the study of formal languages over string case to two dimensional languages or picture languages has been of interest for long for its vast applications. In the thesis and the most common two-dimensional object studied is a picture which is a rectangular array of symbols taken from a finite alphabet. T he objective of this thesis concentrates on the study of generation of Picture language classes by bio-inspired operations namely, `Splicing' and `Self-Assembly' of DNA-Computing. Namely, H-Array Splicing System and Tiling Rule Systems. H-array Splicing Systems is a bio-inspired formalism extended from H-Splicing from string case, a vastly investigated study introduced by T. Head. In particular it is structured as a mechanism by studying two-dimensional right linear grammars. In elaborate this formalism is a mechanism which is applied on finite number of pictures called initial pictures with given set of column and row domino splicing rules. The context site where the two pictures are cut in columns and rows are decided by the sequence of adjacent dominoes in the set of rules. And then the `pasting' of the first part (or sub-array) of the picture to the second part of the picture is done by column and row concatenations respectively. The H-Array Splicing Systems is applied over 2D-RLG languages generating H-Array Splicing languages (HASL). Then the restriction classes defined and study are Self Cross over Arrays and Simple Array Splicing languages and incomparable results are proved with 2D-RLG, HASL. They are not disjoint and they intersect Recognizable languages. Another and the second main formalism introduced and studied in the thesis is Tiling Rule System TRuS . This formalism generates picture by set of tiling rules, assembling tiles. We have proved that the class of L(TS) (Tiling System, recognizable language) is contained in TRuS . Also, we prove there exist a construct of the formalism based on generating pictures in rows or columns which is equivalent to L(TS). The equivalence is proved using Wang systems. Thus leading to an interesting notion of bio-inspired (self-assembling) operation to picture generation

Self-Assembly of Tiles: Theoretical Models, the Power of Signals, and Local Computing

DNA-based self-assembly is an autonomous process whereby a disordered system of DNA sequences forms an organized structure or pattern as a consequence of Watson-Crick complementarity of DNA sequences, without external direction. Here, we propose self-assembly (SA) hypergraph automata as an automata-theoretic model for patterned self-assembly. We investigate the computational power of SA-hypergraph automata and show that for every recognizable picture language, there exists an SA-hypergraph automaton that accepts this language. Conversely, we prove that for any restricted SA-hypergraph automaton, there exists a Wang Tile System, a model for recognizable picture languages, that accepts the same language. Moreover, we investigate the computational power of some variants of the Signal-passing Tile Assembly Model (STAM), as well as propose the concept of {\it Smart Tiles}, i.e., tiles with glues that can be activated or deactivated by signals, and which possess a limited amount of local computing capability. We demonstrate the potential of smart tiles to perform some robotic tasks such as replicating complex shapes

Infinite games with finite knowledge gaps

Infinite games where several players seek to coordinate under imperfect information are deemed to be undecidable, unless the information is hierarchically ordered among the players. We identify a class of games for which joint winning strategies can be constructed effectively without restricting the direction of information flow. Instead, our condition requires that the players attain common knowledge about the actual state of the game over and over again along every play. We show that it is decidable whether a given game satisfies the condition, and prove tight complexity bounds for the strategy synthesis problem under $\omega$-regular winning conditions given by parity automata.Comment: 39 pages; 2nd revision; submitted to Information and Computatio

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