Semantic equivalences are used in process algebra to capture the notion of
similar behaviour, and this paper proposes a semi-quantitative equivalence for
a stochastic process algebra developed for biological modelling. We consider
abstracting away from fast reactions as suggested by the Quasi-Steady-State
Assumption. We define a fast-slow bisimilarity based on this idea. We also show
congruence under an appropriate condition for the cooperation operator of
Bio-PEPA.
The process algebra HYPE was recently proposed as a fine-grained modelling
approach for capturing the behaviour of hybrid systems. In the original
proposal, each flow or influence affecting a variable is modelled separately
and the overall behaviour of the system then emerges as the composition of
these flows. The discrete behaviour of the system is captured by instantaneous
actions which might be urgent, taking effect as soon as some activation
condition is satisfied, or non-urgent meaning that they can tolerate some
(unknown) delay before happening.
Delays in biological systems may be used to model events for which the
underlying dynamics cannot be precisely observed, or to provide abstraction of
some behavior of the system resulting more compact models. In this paper we
enrich the stochastic process algebra Bio-PEPA, with the possibility of
assigning delays to actions, yielding a new non-Markovian process algebra:
Bio-PEPAd. This is a conservative extension meaning that the original syntax of
Bio-PEPA is retained and the delay specification which can now be associated
with actions may be added to existing Bio-PEPA models.
Compositionality is a key feature of process algebras which is often cited as
one of their advantages as a modelling technique. It is certainly true that in
biochemical systems, as in many other systems, model construction is made
easier in a formalism which allows the problem to be tackled compositionally.
In this paper we consider the extent to which the compositional structure which
is inherent in process algebra models of biochemical systems can be exploited
during model solution. In essence this means using the compositional structure
to guide decomposed solution and analysis.