A uniform definition of stochastic process calculi

We introduce a unifying framework to provide the semantics of process algebras, including their quantitative variants useful for modeling quantitative aspects of behaviors. The unifying framework is then used to describe some of the most representative stochastic process algebras. This provides a general and clear support for an understanding of their similarities and differences. The framework is based on State to Function Labeled Transition Systems, FuTSs for short, that are state-transition structures where each transition is a triple of the form (s; α;P). The first andthe second components are the source state, s, and the label, α, of the transition, while the third component is the continuation function, P, associating a value of a suitable type to each state s0. For example, in the case of stochastic process algebras the value of the continuation function on s0 represents the rate of the negative exponential distribution characterizing the duration/delay of the action performed to reach state s0 from s. We first provide the semantics of a simple formalism used to describe Continuous-Time Markov Chains, then we model a number of process algebras that permit parallel composition of models according to the two main interaction paradigms (multiparty and one-to-one synchronization). Finally, we deal with formalisms where actions and rates are kept separate and address the issues related to the coexistence of stochastic, probabilistic, and non-deterministic behaviors. For each formalism, we establish the formal correspondence between the FuTSs semantics and its original semantics

Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically

Labeled state-to-function transition systems, FuTS for short, are characterized by transitions which relate states to functions of states over general semirings, equipped with a rich set of higher-order operators. As such, FuTS constitute a convenient modeling instrument to deal with process languages and their quantitative extensions in particular. In this paper, the notion of bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A correspondence result is established stating that FuTS-bisimilarity coincides with behavioural equivalence of the associated functor. As generic examples, the equivalences underlying substantial fragments of major examples of quantitative process algebras are related to the bisimilarity of specific FuTS. The examples range from a stochastic process language, PEPA, to a language for Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a language for Markov Automata, MAL. The equivalences underlying these languages are related to the bisimilarity of their specific FuTS. By the correspondence result coalgebraic justification of the equivalences of these calculi is obtained. The specific selection of languages, besides covering a large variety of process interaction models and modelling choices involving quantities, allows us to show different classes of FuTS, namely so-called simple FuTS, combined FuTS, nested FuTS, and general FuTS

The Iray Light Transport Simulation and Rendering System

While ray tracing has become increasingly common and path tracing is well understood by now, a major challenge lies in crafting an easy-to-use and efficient system implementing these technologies. Following a purely physically-based paradigm while still allowing for artistic workflows, the Iray light transport simulation and rendering system allows for rendering complex scenes by the push of a button and thus makes accurate light transport simulation widely available. In this document we discuss the challenges and implementation choices that follow from our primary design decisions, demonstrating that such a rendering system can be made a practical, scalable, and efficient real-world application that has been adopted by various companies across many fields and is in use by many industry professionals today

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

Compositional Verification and Optimization of Interactive Markov Chains

Interactive Markov chains (IMC) are compositional behavioural models extending labelled transition systems and continuous-time Markov chains. We provide a framework and algorithms for compositional verification and optimization of IMC with respect to time-bounded properties. Firstly, we give a specification formalism for IMC. Secondly, given a time-bounded property, an IMC component and the assumption that its unknown environment satisfies a given specification, we synthesize a scheduler for the component optimizing the probability that the property is satisfied in any such environment