Franck van Breugel

CONCUR 2008 - Concurrency Theory

This book constitutes the refereed proceedings of the 19th International Conference on Concurrency Theory, CONCUR 2008, held in Toronto, Canada, August 19-22, 2008. The 33 revised full papers presented together with 2 tool papers were carefully reviewed and selected from 120 submissions. The topics include model checking, process calculi, minimization and equivalence checking, types, semantics, probability, bisimulation and simulation, real time, and formal languages.

A behavioural pseudometric for probabilistic transition systems

Discrete notions of behavioural equivalence sit uneasily with semantic models featuring quantitative data, like probabilistic transition systems. In this paper, we present a pseudometric on a class of probabilistic transition systems yielding a quantitative notion of behavioural equivalence. The pseudometric is defined via the terminal coalgebra of a functor based on a metric on the space of Borel probability measures on a metric space. States of a probabilistic transition system have distance 0 if and only if they are probabilistic bisimilar. We also characterize our distance function in terms of a real-valued modal logic.

Non-blocking binary search trees

This paper describes the first complete implementation of a non-blocking binary search tree in an asynchronous shared-memory system using single-word compare-and-swap operations. The implementation is linearizable and tolerates any number of crash failures. Insert and Delete operations that modify different parts of the tree do not interfere with one another, so they can run completely concurrently. Find operations only perform reads of shared memory.

Towards Quantitative Verification of Probabilistic Transition Systems

It has been argued that Boolean-valued logics and associated discrete notions of behavioural equivalence sit uneasily with semantic models featuring quantitative data, like probabilistic transition systems. In this paper we present a pseudometric on a class of reactive probabilistic transition systems yielding a quantitative notion of behavioural equivalence. The pseudometric is defined via the terminal coalgebra of a functor based on the Hutchinson metric on the space of Borel probability measures on a metric space. We also characterize the distance between systems in terms of a real-valued modal logic.

An Algorithm for Quantitative Verification of Probabilistic Transition Systems

In an earlier paper we presented a pseudometric on the class of reactive probabilistic transition systems, yielding a quantitative notion of behavioural equivalence. The pseudometric is defined via the terminal coalgebra of a functor based on the Hutchinson metric on probability measures. In the present paper we give an algorithm, based on linear programming, to calculate the distance between two states up to prescribed degree of accuracy.

Modelling and verifying web service orchestration by means of the concurrency workbench

Verification techniques like model checking, preorder checking and equivalence checking are shown to be relevant to web service orchestration. The Concurrency Workbench of the New Century (CWB) is a verification tool that supports these verification techniques. By means of the Process Algebra Compiler (PAC), the CWB is modified to support the BPE-calculus. The BPE-calculus is a small language, based on BPEL4WS, to express web service orchestration. Both the syntax and the semantics of the BPE-calculus are formally defined. These are subsequently used as input for the PAC. As output, the PAC produces modules that are incorporated into the CWB so that it supports the BPE-calculus and, hence, provides a verification tool for web service orchestration.

Approximating and computing behavioural distances in probabilistic transition systems

In an earlier paper we presented a pseudometric on the states of a probabilistic transition system, yielding a quantitative notion of behavioural equivalence. The behavioural pseudometric was defined via the terminal coalgebra of a functor based on a metric on Borel probability measures. In the present paper we give a polynomial-time algorithm, based on linear programming, to calculate the distances between states up to a prescribed degree of accuracy.

Domain theory, testing and simulation for labelled Markov processes

This paper presents a fundamental study of similarity and bisimilarity for labelled Markov processes (LMPs). The main results characterize similarity as a testing preorder and bisimilarity as a testing equivalence. In general, LMPs are not required to satisfy a finite-branching condition--indeed the state space may be a continuum, with the transitions given by arbitrary probability measures. Nevertheless we show that to characterize bisimilarity it suffices to use finitely-branching labelled trees as tests.Our results involve an interaction between domain theory and measure theory. One of the main technical contributions is to show that a final object in a suitable category of LMPs can be constructed by solving a domain equation D ≃V(D)Act, where V is the probabilistic powerdomain. Given an LMP whose state space is an analytic space, bisimilarity arises as the kernel of the unique map to the final LMP. We also show that the metric for approximate bisimilarity introduced by Desharnais, Gupta, Jagadeesan and Panangaden generates the Lawson topology on the domain D.

On the complexity of computing probabilistic bisimilarity

Probabilistic bisimilarity is a fundamental notion of equivalence on labelled Markov chains. It has a natural generalisation to a probabilistic bisimilarity pseudometric, whose definition involves the Kantorovich metric on probability distributions. The pseudometric has discounted and undiscounted variants, according to whether one discounts the future in observing discrepancies between states. This paper is concerned with the complexity of computing probabilistic bisimilarity and the probabilistic bisimilarity pseudometric on labelled Markov chains. We show that the problem of computing probabilistic bisimilarity is P-hard by reduction from the monotone circuit value problem. We also show that the discounted pseudometric is rational and can be computed exactly in polynomial time using the network simplex algorithm and the continued fraction algorithm. In the undiscounted case we show that the pseudometric is again rational and can be computed exactly in polynomial time using the ellipsoid algorithm. Finally, using the notion of couplings on Markov chains, we show that the pseudometric can be used to compute bounds on the variational distance of trace distributions, which is NP-hard to compute directly.

A behavioural pseudometric for metric labelled transition systems

Metric labelled transition systems are labelled transition systems whose states and actions form (pseudo)metric spaces. These systems can capture a large class of timed transition systems, including systems with uncountably many states and uncountable nondeterminism. In this paper a behavioural pseudometric is introduced for metric labelled transition systems. The behavioural distance between states, a nonnegative real number, captures the similarity of the behaviour of those states. The smaller the distance, the more alike the states are. In particular, the distance between states is 0 iff they are bisimilar. Three different characterisations of this pseudometric are given: a fixed point, a logical and a coinductive characterisation. These generalise the fixed point, logical and coinductive characterisations of bisimilarity.