Definable transductions and weighted logics for texts

AbstractA text is a word together with an additional linear order on it. We study quantitative models for texts, i.e. text series which assign to texts elements of a semiring. We introduce an algebraic notion of recognizability following Reutenauer and Bozapalidis as well as weighted automata for texts combining an automaton model of Lodaya and Weil with a model of Ésik and Németh. After that we show that both formalisms describe the text series definable in a certain fragment of weighted logics as introduced by Droste and Gastin. In order to do so, we study certain definable transductions and show that they are compatible with weighted logics

Weighted Logics for Nested Words and Algebraic Formal Power Series

Nested words, a model for recursive programs proposed by Alur and Madhusudan, have recently gained much interest. In this paper we introduce quantitative extensions and study nested word series which assign to nested words elements of a semiring. We show that regular nested word series coincide with series definable in weighted logics as introduced by Droste and Gastin. For this we establish a connection between nested words and the free bisemigroup. Applying our result, we obtain characterizations of algebraic formal power series in terms of weighted logics. This generalizes results of Lautemann, Schwentick and Therien on context-free languages

Weighted automata and multi-valued logics over arbitrary bounded lattices

AbstractWe show that L-weighted automata, L-rational series, and L-valued monadic second order logic have the same expressive power, for any bounded lattice L and for finite and infinite words. We also prove that aperiodicity, star-freeness, and L-valued first-order and LTL-definability coincide. This extends classical results of Kleene, Büchi–Elgot–Trakhtenbrot, and others to arbitrary bounded lattices, without any distributivity assumption that is fundamental in the theory of weighted automata over semirings. In fact, we obtain these results for large classes of strong bimonoids which properly contain all bounded lattices

Weighted Automata and Logics on Hierarchical Structures and Graphs

Formal language theory, originally developed to model and study our natural spoken languages, is nowadays also put to use in many other fields. These include, but are not limited to, the definition and visualization of programming languages and the examination and verification of algorithms and systems. Formal languages are instrumental in proving the correct behavior of automated systems, e.g., to avoid that a flight guidance system navigates two airplanes too close to each other. This vast field of applications is built upon a very well investigated and coherent theoretical basis. It is the goal of this dissertation to add to this theoretical foundation and to explore ways to make formal languages and their models more expressive. More specifically, we are interested in models that are able to model quantitative features of the behavior of systems. To this end, we define and characterize weighted automata over structures with hierarchical information and over graphs. In particular, we study infinite nested words, operator precedence languages, and finite and infinite graphs. We show Büchi-like results connecting weighted automata and weighted monadic second order (MSO) logic for the respective classes of weighted languages over these structures. As special cases, we obtain Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words. Establishing such a general result for graphs has been an open problem for weighted logics for some time. We conjecture that our techniques can be applied to derive similar equivalence results in other contexts like traces, texts, and distributed systems

Jahresbericht der Research Academy Leipzig 2007

Jahresbericht der Research Academy Leipzig 2007:Inhalt - Die Research Academy Leipzig - Rede zum einjährigen Jubiläum der Gründung der Research Academy Leipzig - Die Vorteile von Promotionsschulen Eine Betreuerperspektive - Fächerübergreifende Qualifikationsmaßnahmen: Die Veranstaltungen der Research Academy Leipzig 2007 - Präsentation in der Öffentlichkeit - Kleinkindbetreuung für Kinder der Doktorandinnen und Doktoranden - Das Graduiertenzentrum Mathematik/Informatik und Naturwissenschaften - Graduiertenschule Leipzig School of Natural Sciences – Building with Molecules and Nano-objects BuildMoNa - Deutsch-Französisches Doktorandenkollegium Statistical Physics of Complex Systems - International Max Planck Research School Mathematics in the Sciences - International Research Training Group Diffusion in Porous Materials - Graduiertenkolleg Analysis, Geometrie und ihre Verbindung zu den Naturwissenschaften - Graduiertenkolleg Wissensrepräsentation - Graduiertenkolleg Mechanistische und Anwendungsaspekte nichtkonventioneller Oxidationsreaktionen - Internationales Promotionsprogramm Forschung in Grenzgebieten der Chemie - Das Graduiertenzentrum Lebenswissenschaften - Graduiertenkolleg Interdisziplinäre Ansätze in den Neurowissenschaften InterNeuro - Graduiertenkolleg Funktion von Aufmerksamkeit bei kognitiven Prozessen - Internationales Promotionsprogramm Von der Signalverarbeitung zum Verhalten IPP Signal - International Max Planck Research School The Leipzig School of Human Origins - MD-PhD-Programm der Universität Leipzig - Graduiertenkolleg Universalität und Diversität: Sprachliche Strukturen und Prozesse - Das Graduiertenzentrum Geistes- und Sozialwissenschaften - Internationales Promotionsprogramm Transnationalisierung und Regionalisierung vom 18. Jahrhundert bis zur Gegenwart - Graduiertenkolleg Bruchzonen der Globalisierung - Deutsch als Fremdsprache Transcultural German Studies - Kultureller Austausch Altertumswissenschaftliche, historische und ethnologische Perspektiven - Praktiken gesellschaftlicher Raumproduktionen in Europa Geographische, historische und soziologische Perspektiven - Bildnachweise - Impressu

Kleene-Schützenberger and Büchi Theorems for Weighted Timed Automata

In 1994, Alur and Dill introduced timed automata as a simple mathematical model for modelling the behaviour of real-time systems. In this thesis, we extend timed automata with weights. More detailed, we equip both the states and transitions of a timed automaton with weights taken from an appropriate mathematical structure. The weight of a transition determines the weight for taking this transition, and the weight of a state determines the weight for letting time elapse in this state. Since the weight for staying in a state depends on time, this model, called weighted timed automata, has many interesting applications, for instance, in operations research and scheduling. We give characterizations for the behaviours of weighted timed automata in terms of rational expressions and logical formulas. These formalisms are useful for the specification of real-time systems with continuous resource consumption. We further investigate the relation between the behaviours of weighted timed automata and timed automata. Finally, we present important decidability results for weighted timed automata