Polynomial Time Decidability of Weighted Synchronization under Partial Observability

We consider weighted automata with both positive and negative integer weights on edges and study the problem of synchronization using adaptive strategies that may only observe whether the current weight-level is negative or nonnegative. We show that the synchronization problem is decidable in polynomial time for deterministic weighted automata

Testing Reactive Probabilistic Processes

We define a testing equivalence in the spirit of De Nicola and Hennessy for reactive probabilistic processes, i.e. for processes where the internal nondeterminism is due to random behaviour. We characterize the testing equivalence in terms of ready-traces. From the characterization it follows that the equivalence is insensitive to the exact moment in time in which an internal probabilistic choice occurs, which is inherent from the original testing equivalence of De Nicola and Hennessy. We also show decidability of the testing equivalence for finite systems for which the complete model may not be known

Synchronizing Data Words for Register Automata

Register automata (RAs) are finite automata extended with a finite set of registers to store and compare data from an infinite domain. We study the concept of synchronizing data words in RAs: does there exist a data word that sends all states of the RA to a single state? For deterministic RAs with k registers (k-DRAs), we prove that inputting data words with 2k+1 distinct data from the infinite data domain is sufficient to synchronize. We show that the synchronization problem for DRAs is in general PSPACE-complete, and it is NLOGSPACE-complete for 1-DRAs. For nondeterministic RAs (NRAs), we show that Ackermann(n) distinct data (where n is the size of the RA) might be necessary to synchronize. The synchronization problem for NRAs is in general undecidable, however, we establish Ackermann-completeness of the problem for 1-NRAs. Another main result is the NEXPTIME-completeness of the length-bounded synchronization problem for NRAs, where a bound on the length of the synchronizing data word, written in binary, is given. A variant of this last construction allows to prove that the length-bounded universality problem for NRAs is co-NEXPTIME-complete

Computation Tree Logic for Synchronization Properties

We present a logic that extends CTL (Computation Tree Logic) with operators that express synchronization properties. A property is synchronized in a system if it holds in all paths of a certain length. The new logic is obtained by using the same path quantifiers and temporal operators as in CTL, but allowing a different order of the quantifiers. This small syntactic variation induces a logic that can express non-regular properties for which known extensions of MSO with equality of path length are undecidable. We show that our variant of CTL is decidable and that the model-checking problem is in Delta_3^P = P^{NP^{NP}}, and is hard for the class of problems solvable in polynomial time using a parallel access to an NP oracle. We analogously consider quantifier exchange in extensions of CTL, and we present operators defined using basic operators of CTL* that express the occurrence of infinitely many synchronization points. We show that the model-checking problem remains in Delta_3^P. The distinguishing power of CTL and of our new logic coincide if the Next operator is allowed in the logics, thus the classical bisimulation quotient can be used for state-space reduction before model checking

Synchronizing automata over nested words

We extend the concept of a synchronizing word from deterministic finite-state automata (DFA) to nested word automata (NWA): A well-matched nested word is called synchronizing if it resets the control state of any configuration, i. e., takes the NWA from all control states to a single control state. We show that although the shortest synchronizing word for an NWA, if it exists, can be (at most) exponential in the size of the NWA, the existence of such a word can still be decided in polynomial time. As our main contribution, we show that deciding the existence of a short synchronizing word (of at most given length) becomes PSPACE-complete (as opposed to NP-complete for DFA). The upper bound makes a connection to pebble games and Strahler numbers, and the lower bound goes via small-cost synchronizing words for DFA, an intermediate problem that we also show PSPACE-complete. We also characterize the complexity of a number of related problems, using the observation that the intersection nonemptiness problem for NWA is EXP-complete

Contribution to the verification of timed automata (determinization, quantitative verification and reachability in networks of automata)

Cette thèse porte sur la vérification des automates temporisés, un modèle bien établi pour les systèmes temps-réels. La thèse est constituée de trois parties. La première est dédiée à la déterminisation des automates temporisés, problème qui n'a pas de solution en général. Nous proposons une méthode approchée (sur-approximation, sous-approximation, mélange des deux) fondée sur la construction d'un jeu de sûreté. Cette méthode améliore les approches existantes en combinant leurs avantages respectifs. Nous appliquons ensuite cette méthode de déterminisation à la génération automatique de tests de conformité. Dans la seconde partie, nous prenons en compte des aspects quantitatifs des systèmes temps-réel grâce à une notion de fréquence des états acceptants dans une exécution d'un automate temporisé. Plus précisément, la fréquence d'une exécution est la proportion de temps passée dans les états acceptants. Nous intéressons alors à l'ensemble des fréquences des exécutions d'un automate temporisé pour étudier, par exemple, le vide de langages seuils. Nous montrons ainsi que les bornes de l'ensemble des fréquences sont calculables pour deux classes d'automates temporisés. D'une part, les bornes peuvent être calculées en espace logarithmique par une procédure non-déterministe dans les automates temporisés à une horloge. D'autre part, elles peuvent être calculées en espace polynomial dans les automates temporisés à plusieurs horloges ne contenant pas de cycles forçant la convergence d'horloges. Finalement, nous étudions le problème de l'accessibilité des états acceptants dans des réseaux d'automates temporisés qui communiquent via des files FIFO. Nous considérons tout d'abord des automates temporisés à temps discret, et caractérisons les topologies de réseaux pour lesquelles l'accessibilité est décidable. Cette caractérisation est ensuite étendue aux automates temporisés à temps continu.This thesis is about verification of timed automata, a well-established model for real time systems. The document is structured in three parts. The first part is dedicated to the determinization of timed automata, a problem which has no solution in general. We propose an approximate (over-approximation/under-approximation/mix) method based on the construction of a safety game. This method improves both existing approaches by combining their respective advantages. Then, we apply this determinization approach to the generation of conformance tests. In the second part, we take into account quantitative aspects of real time systems thanks to a notion of frequency of accepting states along executions of timed automata. More precisely, the frequency of a run is the proportion of time elapsed in accepting states. Then, we study the set of frequencies of runs of a timed automaton in order to decide, for example, the emptiness of threshold languages. We thus prove that the bounds of the set of frequencies are computable for two classes of timed automata. On the one hand, we prove that bounds are computable in logarithmic space by a non-deterministic procedure in one-clock timed automata. On the other hand, they can be computed in polynomial space in timed automata with several clocks, but having no cycle that forces the convergence between clocks. Finally, we study the reachability problem in networks of timed automata communicating through FIFO channels. We first consider dicrete timed automata, and characterize topologies of networks for which reachability is decidable. Then, this characterization is extended to dense-time automata.RENNES1-Bibl. électronique (352382106) / SudocSudocFranceF

A uniform approach to the complexity and analysis of succinct systems

“ This thesis provides a unifying view on the succinctness of systems: the capability of a modeling formalism to describe the behavior of a system of exponential size using a polynomial syntax. The key theoretical contribution is the introduction of sequential circuit machines as a new universal computation model that focuses on succinctness as the central aspect. The thesis demonstrates that many well-known modeling formalisms such as communicating state machines, linear-time temporal logic, or timed automata exhibit an immediate connection to this machine model. Once a (syntactic) connection is established, many complexity bounds for structurally restricted sequential circuit machines can be transferred to a certain formalism in a uniform manner. As a consequence, besides a far-reaching unification of independent lines of research, we are also able to provide matching complexity bounds for various analysis problems, whose complexities were not known so far. For example, we establish matching lower and upper bounds of the small witness problem and several variants of the bounded synthesis problem for timed automata, a particularly important succinct modeling formalism. Also for timed automata, our complexity-theoretic analysis leads to the identification of tractable fragments of the timed synthesis problem under partial observability. Specifically, we identify timed controller synthesis based on discrete or template-based controllers to be equivalent to model checking. Based on this discovery, we develop a new model checking-based algorithm to efficiently find feasible template instantiations. From a more practical perspective, this thesis also studies the preservation of succinctness in analysis algorithms using symbolic data structures. While efficient techniques exist for specific forms of succinctness considered in isolation, we present a general approach based on abstraction refinement to combine off-the-shelf symbolic data structures. In particular, for handling the combination of concurrency and quantitative timing behavior in networks of timed automata, we report on the tool Synthia which combines binary decision diagrams with difference bound matrices. In a comparison with the timed model checker Uppaal and the timed game solver Tiga running on standard benchmarks from the timed model checking and synthesis domain, respectively, the experimental results clearly demonstrate the effectiveness of our new approach.Diese Dissertation liefert eine vereinheitlichende Sicht auf die Kompaktheit von Systemen: die Fähigkeit eines Modellierungsformalismus, das Verhalten eines Systems exponentieller Größe mit polynomieller Syntax zu beschreiben. Der wesentliche theoretische Beitrag ist die Einführung von sequenziellen Schaltkreis-Maschinen als neues universelles Berechnungsmodell, das sich auf den zentralen Aspekt der Kompaktheit konzentriert. Die Dissertation demonstriert, dass viele bekannte Modellierungsformalismen, wie z.B. kommunizierende Zustandsmaschinen, linear-Zeit temporale Logik (LTL) oder gezeitete Automaten eine direkte Verbindung zu diesem Maschinenmodell aufzeigen. Sobald eine (syntaktische) Verbindung hergestellt ist, können viele Komplexitätsschranken für strukturell beschränkte sequenzielle Schaltkreis-Maschinen für einen bestimmten Formalismus einheitlich übernommen werden. Neben einer weitreichenden Vereinheitlichung unabhängiger Forschungsrichtungen können auch zahlreiche Komplexitätsschranken für Analyse-Probleme etabliert werden, deren genaue Komplexität bisher noch nicht bekannt war. Zum Beispiel werden passende untere und obere Schranken des small witness Problems und mehrere Varianten des Synthese-Problems von Controllern mit beschränkter Größe für gezeitete Automaten bewiesen. Die theoretische Analyse deckt Fragmente geringerer Komplexität des partiell informierten Syntheseproblems für gezeitete Automaten auf. Es wird im Besonderen gezeigt, dass das gezeitete Syntheseproblem für diskrete oder Vorlagen-basierte Controller äquivalent zum Model Checking-Problem ist. Basierend auf dieser Einsicht wird ein neuartiger Model Checking-basierter Algorithmus zur effizienten Synthese von gültigen Instantiierungen von Vorlagen entwickelt. Der praktische Beitrag der Dissertation untersucht die Erhaltung von Kompaktheit in Analyse-Algorithmen durch die Benutzung symbolischer Datenstrukturen. Es wird ein allgemeiner Ansatz zur Kombination von Standard-Datenstrukturen vorgestellt, die jeweils bisher nur in Isolation verwendet werden konnten. Insbesondere wird für die Analyse von Netzwerken von gezeiteten Automaten das Tool Synthia vorgestellt, welches binäre Entscheidungs-Diagramme mit Differenzen-Matrizen verbindet. In einem experimentellen Vergleich mit den Tools Uppaal und Tiga wird klar die Effektivität des neuen Ansatzes belegt