Nicolás Wolovick

Measurability and safety verification for stochastic hybrid systems

Dealing with the interplay of randomness and continuous time is important for the formal verification of many real systems. Considering both facets is especially important for wireless sensor networks, distributed control applications, and many other systems of growing importance. An important traditional design and verification goal for such systems is to ensure that unsafe states can never be reached. In the stochastic setting, this translates to the question whether the probability to reach unsafe states remains tolerable. In this paper, we consider stochastic hybrid systems where the continuous-time behaviour is given by differential equations, as for usual hybrid systems, but the targets of discrete jumps are chosen by probability distributions. These distributions may be general measures on state sets. Also non-determinism is supported, and the latter is exploited in an abstraction and evaluation method that establishes safe upper bounds on reachability probabilities. To arrive there requires us to solve semantic intricacies as well as practical problems. In particular, we show that measurability of a complete system follows from the measurability of its constituent parts. On the practical side, we enhance tool support to work effectively on such general models. Experimental evidence is provided demonstrating the applicability of our approach on three case studies, tackled using a prototypical implementation.

A characterization of meaningful schedulers for continuous-time markov decision processes

Continuous-time Markov decision process are an important variant of labelled transition systems having nondeterminism through labels and stochasticity through exponential fire-time distributions. Nondeterministic choices are resolved using the notion of a scheduler. In this paper we characterize the class of measurable schedulers, which is the most general one, and show how a measurable scheduler induces a unique probability measure on the sigma-algebra of infinite paths. We then give evidence that for particular reachability properties it is sufficient to consider a subset of measurable schedulers. Having analyzed schedulers and their induced probability measures we finally show that each probability measure on the sigma-algebra of infinite paths is indeed induced by a measurable scheduler which proves that this class is complete.

Nondeterministic Labeled Markov Processes: Bisimulations and Logical Characterization

We extend the theory of labeled Markov processeswith internal nondeterminism, a fundamental conceptfor the further development of a process theory withabstraction on nondeterministic continuous probabilisticsystems. We define nondeterministic labeled Markovprocesses (NLMP) and provide both a state basedbisimulation and an event based bisimulation. We showthe relation between them, including that the largeststate bisimulation is also an event bisimulation. Wealso introduce a variation of the Hennessy-Milnerlogic that characterizes event bisimulation and that issound w.r.t. the state base bisimulation for arbitraryNLMP. This logic, however, is infinitary as it containsa denumerable ∨. We then introduce a finitary sublogicthat characterize both state and event bisimulation forimage finite NLMP whose underlying measure spaceis also analytic. Hence, in this setting, all notions ofbisimulation we deal with turn out to be equal.

q-state Potts model metastability study using optimized GPU-based Monte Carlo algorithms

Abstract We implemented a GPU-based parallel code to perform Monte Carlo simulations of the two-dimensional q -state Potts model. The algorithm is based on a checkerboard update scheme and assigns independent random number generators to each thread. The implementation allows to simulate systems up to ∼10 9 spins with an average time per spin flip of 0.147 ns on the fastest GPU card tested, representing a speedup up to 155×, compared with an optimized serial code running on a high-end CPU. The possibility of performing high speed simulations at large enough system sizes allowed us to provide a positive numerical evidence about the existence of metastability on very large systems based on Binderʼs criterion, namely, on the existence or not of specific heat singularities at spinodal temperatures different of the transition one.

A Theory for the Semantics of Stochastic and Non-deterministic Continuous Systems

The description of complex systems involving physical or biological components usually requires to model complex continuous behavior induced by variables such as time, distance, speed, temperature, alkalinity of a solution, etc. Often, such variables can be quantified probabilistically to better understand the behavior of the complex systems. For example, the arrival time of events may be considered a Poisson process or the weight of an individual may be assumed to be distributed according to a log-normal distribution. However, it is also common that the uncertainty on how these variables behave makes us prefer to leave out the choice of a particular probability and rather model it as a purely non-deterministic decision, as it is the case when a system is intended to be deployed in a variety of very different computer or network architectures. Therefore, the semantics of these systems needs to be represented by a variant of probabilistic automata that involves continuous domains on the state space and the transition relation. In this paper, we provide a survey on the theory of such kind of models. We present the theory of the so-called labeled Markov processes LMP and its extension with internal non-determinism NLMP. We show that in these complex domains, the bisimulation relation can be understood in different manners. We show the relation between the different bisimulations and try to understand their expressiveness through examples. We also study variants of Hennessy-Milner logic that provides logical characterizations of some of these bisimulations.

Automatic Probabilistic Program Verification through Random Variable Abstraction

The weakest pre-expectation calculus has been proved to be a mature theory to analyze quantitative properties of probabilistic and nondeterministic programs. We present an automatic method for proving quantitative linear properties on any denumerable state space using iterative backwards fixed point calculation in the general framework of abstract interpretation. In order to accomplish this task we present the technique of random variable abstraction (RVA) and we also postulate a sufficient condition to achieve exact fixed point computation in the abstract domain. The feasibility of our approach is shown with two examples, one obtaining the expected running time of a probabilistic program, and the other the expected gain of a gambling strategy. Our method works on general guarded probabilistic and nondeterministic transition systems instead of plain pGCL programs, allowing us to easily model a wide range of systems including distributed ones and unstructured programs. We present the operational and weakest precondition semantics for this programs and prove its equivalence.

The Road from Stochastic Automata to the Simulation of Rare Events

We report in the advances on stochastic automata and its use on rare event simulation. We review and introduce an extension of IOSA, an input/output variant of stochastic automata that under mild constraints can be ensured to contain non-determinism only in a spurious manner. That is, the model can be regarded as fully probabilistic and hence amenable for simulation. We also report on our latest work on fully automatizing the technique of rare event simulation. Using the structure of the model given in terms a network of IOSAs allows us to automatically derive the importance function, which is crucial for the importance splitting technique of rare event simulation. We conclude with experimental results that show how promising our technique is.