A hemimetric extension of simulation for semi-markov decision processes

Semi-Markov decision processes (SMDPs) are continuous-time Markov decision processes where the residence-time on states is governed by generic distributions on the positive real line. In this paper we consider the problem of comparing two SMDPs with respect to their time-dependent behaviour. We propose a hemimetric between processes, which we call simulation distance, measuring the least acceleration factor by which a process needs to speed up its actions in order to behave at least as fast as another process. We show that this distance can be computed in time O(n2(f(l)+k)+mn7), where n is the number of states, m the number of actions, k the number of atomic propositions, and f(l) the complexity of comparing the residence-time between states. The theoretical relevance and applicability of this distance is further argued by showing that (i) it is suitable for compositional reasoning with respect to CSP-like parallel composition and (ii) has a logical characterisation in terms of a simple Markovian logic

Quantitative Graded Semantics and Spectra of Behavioural Metrics

Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition systems. In analogy to the classical linear-time/branching-time spectrum of two-valued behavioural equivalences on transition systems, behavioural metrics come in various degrees of granularity, depending on the observer's ability to interact with the system. Graded monads have been shown to provide a unifying framework for spectra of behavioural equivalences. Here, we transfer this principle to spectra of behavioural metrics, working at a coalgebraic level of generality, that is, parametrically in the system type. In the ensuing development of quantitative graded semantics, we discuss presentations of graded monads on the category of metric spaces in terms of graded quantitative equational theories. Moreover, we obtain a canonical generic notion of invariant real-valued modal logic, and provide criteria for such logics to be expressive in the sense that logical distance coincides with the respective behavioural distance. We thus recover recent expressiveness results for coalgebraic branching-time metrics and for trace distance in metric transition systems; moreover, we obtain a new expressiveness result for trace semantics of fuzzy transition systems. We also provide a number of salient negative results. In particular, we show that trace distance on probabilistic metric transition systems does not admit a characteristic real-valued modal logic at all

Reduction of Nondeterministic Tree Automata

We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It uses criteria based on combinations of downward and upward simulation preorder on trees, and the more general downward and upward language inclusions. Since tree-language inclusion is EXPTIME-complete, we describe methods to compute good approximations in polynomial time. We implemented our algorithm as a module of the well-known libvata tree automata library, and tested its performance on a given collection of tree automata from various applications of libvata in regular model checking and shape analysis, as well as on various classes of randomly generated tree automata. Our algorithm yields substantially smaller and sparser automata than all previously known reduction techniques, and it is still fast enough to handle large instances.Comment: Extended version (including proofs) of material presented at TACAS 201

Conception par composantes de contrôleurs d'usines modulaires utilisant la théorie du contrôle supervisé

La complexité croissante des processus industriels et de leurs systèmes de contrôle rend de plus en plus attrayant l'usage des méthodes formelles pour leur conception. Plusieurs méthodes ont été mises au point tant pour la synthèse que pour la vérification, utilisant divers formalismes pour la modélisation de problèmes de contrôle et le raisonnement. Lorsqu'un processus peut être modélisé sous forme d'un système à événements discrets, la théorie du contrôle supervisé, originalement formulée par Ramadge et Wonham, offre une base formelle intéressante pour la spécification de problèmes de contrôle car elle permet, par l'application de procédures de synthèse, d'obtenir automatiquement un contrôleur pour le processus.La théorie souffre cependant d'un problème d'explosion combinatoire puisqu'elle utilise des automates d'états finis comme formalisme de modélisation. Plusieurs investigations se sont concentrées sur les moyens de mitiger ce problème en prenant avantage, soit de la structure des systèmes modélisés, soit des propriétés de leur spécification. Il en résulte plusieurs formes de la théorie dont, entre autres, les variantes modulaire, répartie et hiérarchique. D'autre part, certains efforts de recherche se sont concentrés sur le problème de l'implémentation des contrôleurs obtenus par les procédures de synthèse de la théorie. Il existe donc à ce jour plusieurs implémentations de ces procédures couvrant toutes les variantes de la théorie. Mais il ne semble pas y avoir encore d'environnement couvrant le processus de conception au complet. Le problème est encore plus aigu si l'on considère que la phase de modélisation est en général mal définie, voire même ignorée, dans ces implémentations.La présente thèse se propose de dégager les principes permettant de concevoir un environnement couvrant l'ensemble du processus d'ingénierie de contrôleurs dans le cadre de la théorie du contrôle supervisé, intégrant un outillage adéquat pour les trois phases du processus : modélisation, synthèse et génération de code

Meaning and Grammar of Nouns and Verbs

The papers collected in this book cover contemporary and original research on semantic and grammatical issues of nouns and noun phrases, verbs and sentences, and aspects of the combination of nouns and verbs, in a great variety of languages. A special focus is put on noun types, tense and aspect semantics, granularity of verb meaning, and subcompositionality. The investigated languages and language groups include Austronesian, East Asian, Slavic, German, English, Hungarian and Lakhota. The collection provided in this book will be of interest to researchers and advanced students specialising in the fields of semantics, morphology, syntax, typology, and cognitive sciences