Weakly-Unambiguous Parikh Automata and Their Link to Holonomic Series

We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of holonomic power series. We first prove a strong version of a conjecture by Castiglione and Massazza: weakly-unambiguous Parikh automata are equivalent to unambiguous two-way reversal bounded counter machines, and their multivariate generating series are holonomic. We then show that the converse is not true: we construct a language whose generating series is algebraic (thus holonomic), but which is inherently weakly-ambiguous as a Parikh automata language. Finally, we prove an effective decidability result for the inclusion problem for weakly-unambiguous Parikh automata, and provide an upper-bound on its complexity

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

Numbers and Languages

The thesis presents results obtained during the authors PhD-studies. First systems of language equations of a simple form consisting of just two equations are proved to be computationally universal. These are systems over unary alphabet, that are seen as systems of equations over natural numbers. The systems contain only an equation X+A=B and an equation X+X+C=X+X+D, where A, B, C and D are eventually periodic constants. It is proved that for every recursive set S there exists natural numbers p and d, and eventually periodic sets A, B, C and D such that a number n is in S if and only if np+d is in the unique solution of the abovementioned system of two equations, so all recursive sets can be represented in an encoded form. It is also proved that all recursive sets cannot be represented as they are, so the encoding is really needed. Furthermore, it is proved that the family of languages generated by Boolean grammars is closed under injective gsm-mappings and inverse gsm-mappings. The arguments apply also for the families of unambiguous Boolean languages, conjunctive languages and unambiguous languages. Finally, characterizations for morphisims preserving subfamilies of context-free languages are presented. It is shown that the families of deterministic and LL context-free languages are closed under codes if and only if they are of bounded deciphering delay. These families are also closed under non-codes, if they map every letter into a submonoid generated by a single word. The family of unambiguous context-free languages is closed under all codes and under the same non-codes as the families of deterministic and LL context-free languages.Siirretty Doriast

26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband

Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft für Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jährliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe Zuverlässige Systeme des Instituts für Informatik an der Christian-Albrechts-Universität Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei Neumünster. Während des Tre↵ens wird ein Workshop für alle Interessierten statt finden. In Tannenfelde werden • Christoph Löding (Aachen) • Tomás Masopust (Dresden) • Henning Schnoor (Kiel) • Nicole Schweikardt (Berlin) • Georg Zetzsche (Paris) eingeladene Vorträge zu ihrer aktuellen Arbeit halten. Darüber hinaus werden 26 Vorträge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthält Kurzfassungen aller Beiträge. Wir danken der Gesellschaft für Informatik, der Christian-Albrechts-Universität zu Kiel und dem Tagungshotel Tannenfelde für die Unterstützung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk

Ambiguity through the lens of measure theory

In this paper, we consider automata accepting irreducible sofic shifts, that is, strongly connected automata where each state is initial and final. We provide a characterization of unambiguity for finite words by means of measure of sets of infinite sequences labelling two runs. More precisely, we show that such an automaton is unambiguous, in the sense that no finite word labels two runs with the same starting state and the same ending state if and only if for each state, the set of infinite sequences labelling two runs starting from that state has measure zero

Automates à contraintes semilinéaires = Automata with a semilinear constraint

Cette thèse présente une étude dans divers domaines de l'informatique théorique de modèles de calculs combinant automates finis et contraintes arithmétiques. Nous nous intéressons aux questions de décidabilité, d'expressivité et de clôture, tout en ouvrant l'étude à la complexité, la logique, l'algèbre et aux applications. Cette étude est présentée au travers de quatre articles de recherche. Le premier article, Affine Parikh Automata, poursuit l'étude de Klaedtke et Ruess des automates de Parikh et en définit des généralisations et restrictions. L'automate de Parikh est un point de départ de cette thèse; nous montrons que ce modèle de calcul est équivalent à l'automate contraint que nous définissons comme un automate qui n'accepte un mot que si le nombre de fois que chaque transition est empruntée répond à une contrainte arithmétique. Ce modèle est naturellement étendu à l'automate de Parikh affine qui effectue une opération affine sur un ensemble de registres lors du franchissement d'une transition. Nous étudions aussi l'automate de Parikh sur lettres: un automate qui n'accepte un mot que si le nombre de fois que chaque lettre y apparaît répond à une contrainte arithmétique. Le deuxième article, Bounded Parikh Automata, étudie les langages bornés des automates de Parikh. Un langage est borné s'il existe des mots w_1, w_2, ..., w_k tels que chaque mot du langage peut s'écrire w_1...w_1w_2...w_2...w_k...w_k. Ces langages sont importants dans des domaines applicatifs et présentent usuellement de bonnes propriétés théoriques. Nous montrons que dans le contexte des langages bornés, le déterminisme n'influence pas l'expressivité des automates de Parikh. Le troisième article, Unambiguous Constrained Automata, introduit les automates contraints non ambigus, c'est-à-dire pour lesquels il n'existe qu'un chemin acceptant par mot reconnu par l'automate. Nous montrons qu'il s'agit d'un modèle combinant une meilleure expressivité et de meilleures propriétés de clôture que l'automate contraint déterministe. Le problème de déterminer si le langage d'un automate contraint non ambigu est régulier est montré décidable. Le quatrième article, Algebra and Complexity Meet Contrained Automata, présente une étude des représentations algébriques qu'admettent les automates contraints et les automates de Parikh affines. Nous déduisons de ces caractérisations des résultats d'expressivité et de complexité. Nous montrons aussi que certaines hypothèses classiques en complexité computationelle sont reliées à des résultats de séparation et de non clôture dans les automates de Parikh affines. La thèse est conclue par une ouverture à un possible approfondissement, au travers d'un certain nombre de problèmes ouverts.This thesis presents a study from the theoretical computer science perspective of computing models combining finite automata and arithmetic constraints. We focus on decidability questions, expressiveness, and closure properties, while opening the study to complexity, logic, algebra, and applications. This thesis is presented through four research articles. The first article, Affine Parikh Automata, continues the study of Klaedtke and Ruess on Parikh automata and defines generalizations and restrictions of this model. The Parikh automaton is one of the starting points of this thesis. We show that this model of computation is equivalent to the constrained automaton that we define as an automaton which accepts a word only if the number of times each transition is taken satisfies a given arithmetic constraint. This model is naturally extended to affine Parikh automata, in which an affine transformation is applied to a set of registers on taking a transition. We also study the Parikh automaton on letters, that is, an automaton which accepts a word only if the number of times each letter appears in the word verifies an arithmetic constraint. The second article, Bounded Parikh Automata, focuses on the bounded languages of Parikh automata. A language is bounded if there are words w_1, w_2, ..., w_k such that every word in the language can be written as w_1...w_1w_2...w_2 ... w_k...w_k. These languages are important in applications and usually display good theoretical properties. We show that, over the bounded languages, determinism does not influence the expressiveness of Parikh automata. The third article, Unambiguous Constrained Automata, introduces the concept of unambiguity in constrained automata. An automaton is unambiguous if there is only one accepting path per word of its language. We show that the unambiguous constrained automaton is an appealing model of computation which combines a better expressiveness and better closure properties than the deterministic constrained automaton. We show that it is decidable whether the language of an unambiguous constrained automaton is regular. The fourth article, Algebra and Complexity Meet Constrained Automata, presents a study of algebraic representations of constrained automata and affine Parikh automata. We deduce expressiveness and complexity results from these characterizations. We also study how classical computational complexity hypotheses help in showing separations and nonclosure properties in affine Parikh automata. The thesis is concluded by a presentation of possible future avenues of research, through several open problems