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

From Absolute Mind to Zombie: Is Artificial Intelligence Possible?

The dream of achieving artificial intelligence (AI) and, in particular, artificial consciousness (‘strong AI’), is reflected in mythologies and popular culture as utopia and dystopia. This article discusses its conceptual possibility. It first relates the desire to realise strong AI to a self-perception of humanity as opposed to nature, metaphorically represented as gods or God. The realisation of strong AI is perceived as an ultimate victory on nature or God because it represents the crown of creation or evolution: conscious intelligence. The paper proceeds to summarise two debates relevant to AI: one educational and one technological. The technological debate, almost invariably presupposing a materialist framework, is related to the mind–body problem of philosophy; the educational one to understanding the concept of intelligence. By proposing a definition of intelligence linked to an idealist conception of reality, postulating mind as participation in Absolute Mind, I attempt a convergence of these debates, rejecting the possibility of strong AI

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

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

Symmetric Functionals over Tensor Product Spaces in the Context of Quantum Information Theory

This thesis consists of three parts. We begin our investigation with a brief introduction into open quantum systems. Then we explain different measures of distinguishability of density operators, especially the Uhlmann Fidelity, which will be the basis for the model function we investigate in this work. We continue by explaining the time evolution of open quantum systems in more detail, and introducing the important notion of quantum channels as a concept in quantum information theory. This allows us to state a central problem of quantum information theory: the characterization of the quantum information capacity of a given quantum channel. The major challenge is the maximization of the coherent information, a function defined on a n-fold tensor product of a Hilbert space, which is non-additive and thus has to be considered in the limit as n→∞. To gain an insight into this unsolved problem, we study the channel fidelity of a quantum channel, which is a simpler function, also defined on n-fold tensor product spaces. It shares an essential feature with the coherent information in being non-additive. However, in contrast to the coherent information it is mathematically accessible. We establish the channel fidelity as a model for the coherent information and study its properties. In the second part, a short introduction to the representation theory of symmetric and unitary groups is followed by concrete instructions for Collins' and \'{S}niady's formula for the integration of functions of matrix elements of unitary groups with respect to the Haar measure. This exposition culminates in a simplification of the general formula that is optimal for investigating the channel fidelity. In the third part, we calculate channel fidelity moments for arbitrary n. In order to obtain more concrete results, we restrict ourselves to the study of Pauli channels. For these we discuss the transition of the average and variance from small n to the limit n→∞ and give an explicit formula for both in this limit. In particular, we find that for a large number n of Pauli channels, the channel fidelity distribution is peaked very strongly. Additionally, under certain restrictions, the simplified formula from part two also allows us to give concrete expressions for higher moments in the limit n→∞. We conclude by comparing our new results with results from a former work, where, in the search for maximizing states of the channel fidelity, we found states that maximize the channel fidelity of Pauli channels, at least locally. Because these local maxima have a much higher fidelity than the average of the very strongly peaked distribution, we infer that these states would not be found by a standard numerical maximization procedure. If the channel fidelity models the coherent information accurately in this regard, its maximization thus poses a very hard problem

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