Constraint-oriented specification of performance aspects

This note sketches how to extend (distributed) system specifications with performance constraints. The emphasis is on how to include performance aspects in a modular way. The key of the approach is to specify random delays as separated processes that are composed in parallel with an untimed, functional system specification. The use of parallel processes as separate constraints is in accordance with the constraint-oriented specification style as originally proposed by Vissers et al

Counterexample Generation in Probabilistic Model Checking

Providing evidence for the refutation of a property is an essential, if not the most important, feature of model checking. This paper considers algorithms for counterexample generation for probabilistic CTL formulae in discrete-time Markov chains. Finding the strongest evidence (i.e., the most probable path) violating a (bounded) until-formula is shown to be reducible to a single-source (hop-constrained) shortest path problem. Counterexamples of smallest size that deviate most from the required probability bound can be obtained by applying (small amendments to) k-shortest (hop-constrained) paths algorithms. These results can be extended to Markov chains with rewards, to LTL model checking, and are useful for Markov decision processes. Experimental results show that typically the size of a counterexample is excessive. To obtain much more compact representations, we present a simple algorithm to generate (minimal) regular expressions that can act as counterexamples. The feasibility of our approach is illustrated by means of two communication protocols: leader election in an anonymous ring network and the Crowds protocol

A model checker for performance and dependability properties

Markov chains are widely used in the context of performance and reliability evaluation of systems of various nature. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both the discrete [8] and the continuous time setting [1], [3]. In this short paper, we describe the prototype model checker $E \vdash M C^2$ for discrete and continuous-time Markov chains, where properties are expressed in appropriate extensions of CTL.We illustrate the general benefits of this approach and discuss the structure of the tool

A tool for model-checking Markov chains

Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EÎMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EÎMC2

Probably on time and within budget: on reachability in priced probabilistic timed automata

This paper presents an algorithm for cost-bounded probabilistic reachability in timed automata extended with prices (on edges and locations) and discrete probabilistic branching. The algorithm determines whether the probability to reach a (set of) goal location(s) within a given price bound (and time bound) can exceed a threshold p in [0,1]. We prove that the algorithm is partially correct and show an example for which termination cannot be guaranteed

On Generative Parallel Composition

A major reason for studying probabilistic processes is to establish a link between a formal model for describing functional system behaviour and a stochastic process. Compositionality is an essential ingredient for specifying systems. Parallel composition in a probabilistic setting is complicated since it gives rise to non-determinism, for instance due to interleaving of independent autonomous activities. This paper presents a detailed study of the resolution of non-determinism in an asynchronous generative setting. Based on the intuition behind the synchronous probabilistic calculus PCCS we formulate two criteria that an asynchronous parallel composition should fulfill. We provide novel probabilistic variants of parallel composition for CCS and CSP and show that these operators satisfy these general criteria, opposed to most existing proposals. Probabilistic bisimulation is shown to be a congruence for these operators and their expansion is addressed.\ud \ud We would like to thank the reviewers for their constructive criticism and for pointing out the relation between BPTSs and the model of Pnueli and Zuck. We also thank Ed Brinksma and Rom Langerak (both of the University of Twente) for fruitful discussions