Automata and temporal logic over arbitrary linear time

Linear temporal logic was introduced in order to reason about reactive systems. It is often considered with respect to infinite words, to specify the behaviour of long-running systems. One can consider more general models for linear time, using words indexed by arbitrary linear orderings. We investigate the connections between temporal logic and automata on linear orderings, as introduced by Bruy\`ere and Carton. We provide a doubly exponential procedure to compute from any LTL formula with Until, Since, and the Stavi connectives an automaton that decides whether that formula holds on the input word. In particular, since the emptiness problem for these automata is decidable, this transformation gives a decision procedure for the satisfiability of the logic

How do we remember the past in randomised strategies?

Graph games of infinite length are a natural model for open reactive processes: one player represents the controller, trying to ensure a given specification, and the other represents a hostile environment. The evolution of the system depends on the decisions of both players, supplemented by chance. In this work, we focus on the notion of randomised strategy. More specifically, we show that three natural definitions may lead to very different results: in the most general cases, an almost-surely winning situation may become almost-surely losing if the player is only allowed to use a weaker notion of strategy. In more reasonable settings, translations exist, but they require infinite memory, even in simple cases. Finally, some traditional problems becomes undecidable for the strongest type of strategies

Jeux et automates sur les ordres

This thesis relates to automata theory, logics, and game theory. These domains are at the core of theoretical computer science, and research in these areas are motivated in part by system modeling and verification questions. The first part of the thesis considers finite automata and temporal logic on arbitrary linear orderings. We give a procedure to decide satisfiability of an LTL formula, with a doubly exponential space complexity. It transforms a formula into a synchronous transducer in order to check its satisfiability. The second part focuses on games of ordinal length. We introduce a model of two player games on finite arenas, and show that the winner of these games can be decided in polynomial space. Moreover, we show that the winning player has finite state winning strategies.Cette thèse aborde des sujets liés à la théorie des automates, à la logique et à la théorie des jeux. Ces thèmes sont au cœur de l'informatique théorique depuis de nombreuses décennies. Les travaux de recherche dans ces domaines sont motivés entre autres par des questions de modélisation et de vérification de systèmes. La première partie de la thèse considère les automates finis et la logique temporelle sur des ordres linéaires arbitraires. On y donne une procédure (doublement exponentielle en espace) pour décider la satisfaisabilité d'une formule LTL, utilisant une étape de transformation d'une formule logique en un transducteur synchrone. La seconde partie s'intéresse à des jeux de longueur ordinale. On propose un modèle de jeux à deux joueurs sur des graphes finis, et on montre que la question du vainqueur pour ces jeux peut être résolue en espace polynomial. De plus, on montre qu'il existe des stratégies gagnantes à mémoire finie

Graph Games On Ordinals

We consider an extension of Church’s synthesis problem to ordinals by adding limit transitions to graph games. We consider game arenas where these limit transitions are defined using the sets of cofinalstates. Inapreviouspaper,wehaveshownthatsuchgamesofordinallength aredetermined andthatthewinnerproblemis PSPACE-complete, forasubclassofarenaswherethelengthofplays is always smaller than ω ω. However, the proof uses a rather involved reduction to classical Muller games, and theresulting strategies need infinite memory. WeadapttheLARreductionto prove thedeterminacyinthegeneralcase,andtogenerate strategies with finite memory, using a reduction to games where the limit transitions are defined by priorities. We provide an algorithm for computing the winning regions of both players in these games, with a complexity similar to parity games. Its analysis yields three results: determinacy without hypothesis on the length of the plays, existence of memoryless strategies, and membership of the winner problem in NP ∩ co-NP

Deterministic Automata on Unranked Trees

Abstract. We investigate bottom-up and top-down deterministic au-tomata on unranked trees. We show that for an appropriate denition of bottom-up deterministic automata it is possible to minimize the number of states eciently and to obtain a unique canonical representative of the accepted tree language. For top-down deterministic automata it is well known that they are less expressive than the non-deterministic ones. By generalizing a corresponding proof from the theory of ranked tree au-tomata we show that it is decidable whether a given regular language of unranked trees can be recognized by a top-down deterministic au-tomaton. The standard deterministic top-down model is slightly weaker than the model we use, where at each node the automaton can scan the sequence of the labels of its successors before deciding its next move.

Seafarers in Kiribati - Consequences of International labour circulation

Research on seafarers has not been a common theme in migration discourse. Yet, seafarers are a unique occupational group, and an increasing number are recruited from developing countries, such as Kiribati. The majority being men, they are recruited by international agencies for contract work on board ships of different kinds, registered under so called "foreign flags", and travel globally. Seafarers from Kiribati circulate between home islands and spaces that are denationalised and often occupied by different nationalities. Research on seafarers can therefore be placed at the peripheries of discussions on transnational research. The argument in my thesis is that socio-cultural, economic and environmental factors in Kiribati are closely linked to each other. The strong sense of being I-Kiribati (descending from Kiribati) and the cultural meanings of te aomata (being a real person), as being linked to a genealogy, being land to strangers, hard working, resilient and being able to face hardship, influence the likelihood of employment with German and Japanese agencies. The cultural background, together with the physical strength of I-Kiribati men, makes them globally competitive when an excellent standard of education is provided. The Marine and Fishery Training Centres are internationally recognised and are the largest maritime Training Centres in the Pacific. However, seafarers cannot build a transnational network, as they are temporarily migrating out of their cultural framework and their extended family system, moving transversally across maritime areas in the world. This thesis explores how the special form of mobility and the evolving, yet incomplete, articulation of transnationalism affects the social, economic and personal life of seafarers and families remaining in Kiribati. It also investigates the changes of identities that develop through a repetitive change of cultural backgrounds. Research, including six months of fieldwork on different islands in Kiribati, was aimed at understanding the consequences of the temporary absence and presence of seafarers for extended families and their communities; how the employment effects the health and wellbeing of seafarers and their family members; and the impact of remittances on families, communities and the environment in Kiribati. It was also aimed at illuminating whether and where the employment has influenced some of the cultural elements in which I-Kiribati seafarers are embedded