Carron Shankland

A Symbolic Semantics and Bisimulation for Full LOTOS

A symbolic semantics for Full LOTOS in terms of symbolic transition systems is defined; the semantics extends the (infinitely branching) standard semantics by giving meaning to data parameterised behaviours, and provides a finitely branching representation for behaviours. Symbolic bisimulation is defined. This extends our previous work [14], making the definitions more amenable to automated reasoning and processes with recursion.

The tree identify protocol of IEEE 1394 in

Abstract. We specify the tree identify protocol of the IEEE 1394 high performance serial multimedia bus at three different levels of detail using μCRL. We use the cones and foci verification technique of Groote and Springintveld to show that the descriptions are equivalent under branching bisimulation, thereby demonstrating that the protocol behaves as expected.

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Symbolic transition systems separate data from process behaviour by allowing the data to be uninstantiated Designing a HML like modal logic for these transition systems is interesting because of the subtle interplay between the quanti ers for the data and the modal operators quanti ers on transitions This paper presents the syntax and semantics of such a logic and discusses the design issues involved in its construction The logic has been shown to be adequate with respect to strong early bisimulation over symbolic transition systems derived from Full LOTOS We de ne what is meant by adequacy and discuss how we can reason about it with the aid of a mechanised theorem prover

CRL

We introduce a series of descriptions of disease spread using the process algebra WSCCS and compare the derived mean field equations with the traditional ordinary differential equation model. Even the preliminary work presented here brings to light interesting theoretical questions about the “best” way to defined the model.

A Modal Logic for Full LOTOS based on Symbolic Transition Systems

It is well understood that populations cannot grow without bound and that it is competition between individuals for resources which restricts growth. Despite centuries of interest, the question of how best to model density dependent population growth still has no definitive answer. We address this question here through a number of individual based models of populations expressed using the process algebra WSCCS. The advantage of these models is that they can be explicitly based on observations of individual interactions. From our probabilistic models we derive equations expressing overall population dynamics, using a formal and rigorous rewriting based method. These equations are easily compared with the traditionally used deterministic Ordinary Differential Equation models and allow evaluation of those ODE models, challenging their assumptions about system dynamics. Further, the approach is applied to epidemiology, combining population growth with disease spread.

Developing the use of process algebra in the derivation and analysis of mathematical models of infectious disease

A new semantics in terms of mean field equations is presented for WSCCS (Weighted Synchronous Calculus of Communicating Systems). The semantics captures the average behaviour of the system over time, but without computing the entire state space, therefore avoiding the state space explosion problem. This allows easy investigation of models with large numbers of components. The new semantics is shown to be equivalent to the standard Discrete Time Markov Chain semantics of WSCCS as the number of processes tends to infinity. The method of deriving the semantics is illustrated with examples drawn from biology and from computing.

Process Algebra Models of Population Dynamics

We present two individual based models of disease systems using PEPA (Performance Evaluation Process Algebra). The models explore contrasting mechanisms of disease transmission: direct transmission (e.g. measles) and indirect transmission (e.g. malaria, via mosquitos). We extract ordinary differential equations (ODEs) as a continuous approximation to the PEPA models using the Hillston method and compare these with the traditionally used ODE disease models and with the results of stochastic simulation. Improvements to the Hillston method of ODE extraction for this context are proposed, and the new results compare favourably with stochastic simulation results and to ODEs derived for equivalent models in WSCCS (Weighted Synchronous Calculus of Communicating Systems).

From individuals to populations: A mean field semantics for process algebra

A symbolic semantics for Full LOTOS in terms of symbolic transition systems is defined, following the approach taken for message passing CCS in [HL95a], altered to take account of the particular features of LOTOS (multi-way synchronisation, value negotiation, selection predicates). Symbolic bisimulation over symbolic transition systems is defined, and symbolic bisimulation on ground behaviour expressions is shown to preserve the usual concrete (strong) bisimulation on the standard semantics. Finally, a modal logic based on symbolic transition systems is defined. All are illustrated with reference to examples.

Improved Continuous Approximation of PEPA Models through Epidemiological Examples

We present a novel result for a logic for symbolic transition systems based on LOTOS processes. The logic is adequate with respect to bisimulation defined on symbolic transition systems.

Symbolic Bisimulation for Full LOTOS

Abstract. We present an abstract model of the leader election protocol used in the IEEE 1394 High Performance Serial Bus standard. The model is expressed in the probabilistic Guarded Command Language. By formal reasoning based on this description, we establish the probability of the root contention part of the protocol successfully terminating in terms of the number of attempts to do so. Some simple calculations then allow us to establish an upper bound on the time taken for those attempts.