Synthesising Strategy Improvement and Recursive Algorithms for Solving 2.5 Player Parity Games

2.5 player parity games combine the challenges posed by 2.5 player reachability games and the qualitative analysis of parity games. These two types of problems are best approached with different types of algorithms: strategy improvement algorithms for 2.5 player reachability games and recursive algorithms for the qualitative analysis of parity games. We present a method that - in contrast to existing techniques - tackles both aspects with the best suited approach and works exclusively on the 2.5 player game itself. The resulting technique is powerful enough to handle games with several million states

Transient Reward Approximation for Continuous-Time Markov Chains

We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.Comment: Accepted for publication in IEEE Transactions on Reliabilit

Symblicit Exploration and Elimination for Probabilistic Model Checking

Binary decision diagrams can compactly represent vast sets of states, mitigating the state space explosion problem in model checking. Probabilistic systems, however, require multi-terminal diagrams storing rational numbers. They are inefficient for models with many distinct probabilities and for iterative numeric algorithms like value iteration. In this paper, we present a new "symblicit" approach to checking Markov chains and related probabilistic models: We first generate a decision diagram that symbolically collects all reachable states and their predecessors. We then concretise states one-by-one into an explicit partial state space representation. Whenever all predecessors of a state have been concretised, we eliminate it from the explicit state space in a way that preserves all relevant probabilities and rewards. We thus keep few explicit states in memory at any time. Experiments show that very large models can be model-checked in this way with very low memory consumption

Lazy Probabilistic Model Checking without Determinisation

The bottleneck in the quantitative analysis of Markov chains and Markov decision processes against specifications given in LTL or as some form of nondeterministic B\"uchi automata is the inclusion of a determinisation step of the automaton under consideration. In this paper, we show that full determinisation can be avoided: subset and breakpoint constructions suffice. We have implemented our approach---both explicit and symbolic versions---in a prototype tool. Our experiments show that our prototype can compete with mature tools like PRISM.Comment: 38 pages. Updated version for introducing the following changes: - general improvement on paper presentation; - extension of the approach to avoid full determinisation; - added proofs for such an extension; - added case studies; - updated old case studies to reflect the added extensio

Model checking stochastic hybrid systems

The interplay of random phenomena with discrete-continuous dynamics deserves increased attention in many systems of growing importance. Their verification needs to consider both stochastic behaviour and hybrid dynamics. In the verification of classical hybrid systems, one is often interested in deciding whether unsafe system states can be reached. In the stochastic setting, we ask instead whether the probability of reaching particular states is bounded by a given threshold. In this thesis, we consider stochastic hybrid systems and develop a general abstraction framework for deciding such problems. This gives rise to the first mechanisable technique that can, in practice, formally verify safety properties of systems which feature all the relevant aspects of nondeterminism, general continuous-time dynamics, and probabilistic behaviour. Being based on tools for classical hybrid systems, future improvements in the effectiveness of such tools directly carry over to improvements in the effectiveness of our technique. We extend the method in several directions. Firstly, we discuss how we can handle continuous probability distributions. We then consider systems which we are in partial control of. Next, we consider systems in which probabilities are parametric, to analyse entire system families at once. Afterwards, we consider systems equipped with rewards, modelling costs or bonuses. Finally, we consider all orthogonal combinations of the extensions to the core model.In vielen Systemen wachsender Bedeutung tritt zufallsabhängiges Verhalten gleichzeitig mit diskret-kontinuierlicher Dynamik auf. Um solche Systeme zu verifizieren, müssen sowohl ihr stochastisches Verhalten als auch ihre hybride Dynamik betrachtet werden. In der Analyse klassischer hybrider Systeme ist eine wichtige Frage, ob unsichere Zustände erreicht werden können. Im stochastischen Fall fragen wir stattdessen nach garantierten Wahrscheinlichkeitsschranken. In dieser Arbeit betrachten wir stochastische hybride Systeme und entwickeln eine allgemeine Abstraktionsmethode um Probleme dieser Art zu entscheiden. Dies ermöglicht die erste automatische und praktisch anwendbare Methode, die Sicherheitseigenschaften von Systeme beweisen kann, in denen Nichtdeterminismus, komplexe Dynamik und probabilistisches Verhalten gleichzeitig auftreten. Da die Methode auf Analysetechniken für nichtstochastische hybride Systeme beruht, profitieren wir sofort von zukünftigen Verbesserungen dieser Verfahren. Wir erweitern diese Grundmethode in mehrere Richtungen: Zunächst ergänzen wir das Modell um kontinuierliche Wahrscheinlichkeitsverteilungen. Dann betrachten wir partiell kontrollierbare Systeme. Als nächstes untersuchen wir parametrische Systeme, um eine Klasse ähnlicher Modelle gleichzeitig behandeln. Anschließend betrachten wir Eigenschaften, die auf der Abwägung von Kosten und Nutzen beruhen. Schließlich zeigen wir, wie diese Erweiterungen orthogonal kombiniert werden können

ISCASMC: A Web-Based Probabilistic Model Checker

We introduce the web-based model checker iscasMc for probabilistic systems (see http://iscasmc.ios.ac.cn/IscasMC). This Java application offers an easy-to-use web interface for the evaluation of Markov chains and decision processes against PCTL and PCTL specifications. Compared to PRISM or MRMC, iscasMc is particularly efficient in evaluating the probabilities of LTL properties. © 2014 Springer International Publishing Switzerland.We introduce the web-based model checker iscasMc for probabilistic systems (see http://iscasmc.ios.ac.cn/IscasMC). This Java application offers an easy-to-use web interface for the evaluation of Markov chains and decision processes against PCTL and PCTL specifications. Compared to PRISM or MRMC, iscasMc is particularly efficient in evaluating the probabilities of LTL properties. © 2014 Springer International Publishing Switzerland