Distributed Markovian Bisimulation Reduction aimed at CSL Model Checking

The verification of quantitative aspects like performance and dependability by means of model checking has become an important and vivid area of research over the past decade.\ud \ud An important result of that research is the logic CSL (continuous stochastic logic) and its corresponding model checking algorithms. The evaluation of properties expressed in CSL makes it necessary to solve large systems of linear (differential) equations, usually by means of numerical analysis. Both the inherent time and space complexity of the numerical algorithms make it practically infeasible to model check systems with more than 100 million states, whereas realistic system models may have billions of states.\ud \ud To overcome this severe restriction, it is important to be able to replace the original state space with a probabilistically equivalent, but smaller one. The most prominent equivalence relation is bisimulation, for which also a stochastic variant exists (Markovian bisimulation). In many cases, this bisimulation allows for a substantial reduction of the state space size. But, these savings in space come at the cost of an increased time complexity. Therefore in this paper a new distributed signature-based algorithm for the computation of the bisimulation quotient of a given state space is introduced.\ud \ud To demonstrate the feasibility of our approach in both a sequential, and more important, in a distributed setting, we have performed a number of case studies

Formal analysis techniques for gossiping protocols

We give a survey of formal verification techniques that can be used to corroborate existing experimental results for gossiping protocols in a rigorous manner. We present properties of interest for gossiping protocols and discuss how various formal evaluation techniques can be employed to predict them

Cost Preserving Bisimulations for Probabilistic Automata

Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference notion for summarising the effect of abstraction. This paper considers probabilistic automata augmented with costs. It extends the notions of weak transitions in probabilistic automata in such a way that the costs incurred along a weak transition are captured. This gives rise to cost-preserving and cost-bounding variations of weak probabilistic bisimilarity, for which we establish compositionality properties with respect to parallel composition. Furthermore, polynomial-time decision algorithms are proposed, that can be effectively used to compute reward-bounding abstractions of Markov decision processes in a compositional manner

Extending the Logic IM-SPDL with Impulse and State Rewards

This report presents the logic SDRL (Stochastic Dynamic Reward Logic), an extension of the stochastic logic IM-SPDL, which supports the specication of complex performance and dependability requirements. SDRL extends IM-SPDL with the possibility to express impulse- and state reward measures.\ud The logic is interpreted over extended action-based Markov reward model (EMRM), i.e. transition systems containing both immediate and Markovian transitions, where additionally the states and transitions can be enriched with rewards.\ud We define ne the syntax and semantics of the new logic and show that SDRL provides powerful means to specify path-based properties with timing and reward-based restrictions.\ud In general, paths can be characterised by regular expressions, also called programs, where the executability of a program may depend on the validity of test formulae. For the model checking of SDRL time- and reward-bounded path formulae, a deterministic program automaton is constructed from the requirement. Afterwards the product transition\ud system between this automaton and the EMRM is built and subsequently transformed into a continuous time Markov reward model (MRM) on which numerical\ud analysis is performed.\u

Bisimulation minimisations for Boolean equation systems

Boolean equation systems (BESs) have been used to encode several complex verification problems, including model checking and equivalence checking. We introduce the concepts of strong bisimulation and oblivious bisimulation for BESs, and we prove that these can be used for minimising BESs prior to solving these. Our results show that large reductions of the BESs may be obtained efficiently. Minimisation is rewarding for BESs with non-trivial alternations: the time required for solving the original BES exceeds the time required for quotienting plus the time for solving the quotient. Furthermore, we provide a verification example that demonstrates that bisimulation minimisation of a process prior to encoding the verification problem on that process as a BES can be arbitrarily less effective than minimising the BES that encodes the verification problem

A tutorial on interactive Markov chains

Interactive Markov chains (IMCs) constitute a powerful sto- chastic model that extends both continuous-time Markov chains and labelled transition systems. IMCs enable a wide range of modelling and analysis techniques and serve as a semantic model for many industrial and scientific formalisms, such as AADL, GSPNs and many more. Applications cover various engineering contexts ranging from industrial system-on-chip manufacturing to satellite designs. We present a survey of the state-of-the-art in modelling and analysis of IMCs.\ud We cover a set of techniques that can be utilised for compositional modelling, state space generation and reduction, and model checking. The significance of the presented material and corresponding tools is highlighted through multiple case studies