1,766 research outputs found
Bisimulation of Labeled State-to-Function Transition Systems of Stochastic Process Languages
Labeled state-to-function transition systems, FuTS for short, admit multiple
transition schemes from states to functions of finite support over general
semirings. As such they constitute a convenient modeling instrument to deal
with stochastic process languages. In this paper, the notion of bisimulation
induced by a FuTS is proposed and a correspondence result is proven stating
that FuTS-bisimulation coincides with the behavioral equivalence of the
associated functor. As generic examples, the concrete existing equivalences for
the core of the process algebras ACP, PEPA and IMC are related to the
bisimulation of specific FuTS, providing via the correspondence result
coalgebraic justification of the equivalences of these calculi.Comment: In Proceedings ACCAT 2012, arXiv:1208.430
Investigating modularity in the analysis of process algebra models of biochemical systems
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.
Unfortunately the dynamic behaviour of biochemical systems exhibits strong
interdependencies between the components of the model making decomposed
solution a difficult task. Nevertheless we believe that if such decomposition
based on process algebras could be established it would demonstrate substantial
benefits for systems biology modelling. In this paper we present our
preliminary investigations based on a case study of the pheromone pathway in
yeast, modelling in the stochastic process algebra Bio-PEPA
Bisimulation of Labelled State-to-Function Transition Systems Coalgebraically
Labeled state-to-function transition systems, FuTS for short, are
characterized by transitions which relate states to functions of states over
general semirings, equipped with a rich set of higher-order operators. As such,
FuTS constitute a convenient modeling instrument to deal with process languages
and their quantitative extensions in particular. In this paper, the notion of
bisimulation induced by a FuTS is addressed from a coalgebraic point of view. A
correspondence result is established stating that FuTS-bisimilarity coincides
with behavioural equivalence of the associated functor. As generic examples,
the equivalences underlying substantial fragments of major examples of
quantitative process algebras are related to the bisimilarity of specific FuTS.
The examples range from a stochastic process language, PEPA, to a language for
Interactive Markov Chains, IML, a (discrete) timed process language, TPC, and a
language for Markov Automata, MAL. The equivalences underlying these languages
are related to the bisimilarity of their specific FuTS. By the correspondence
result coalgebraic justification of the equivalences of these calculi is
obtained. The specific selection of languages, besides covering a large variety
of process interaction models and modelling choices involving quantities,
allows us to show different classes of FuTS, namely so-called simple FuTS,
combined FuTS, nested FuTS, and general FuTS
Design and Development of Software Tools for Bio-PEPA
This paper surveys the design of software tools for the Bio-PEPA process algebra. Bio-PEPA is a high-level language for modelling biological systems such as metabolic pathways and other biochemical reaction networks. Through providing tools for this modelling language we hope to allow easier use of a range of simulators and model-checkers thereby freeing the modeller from the responsibility of developing a custom simulator for the problem of interest. Further, by providing mappings to a range of different analysis tools the Bio-PEPA language allows modellers to compare analysis results which have been computed using independent numerical analysers, which enhances the reliability and robustness of the results computed.
Amalgamation of Transition Sequences in the PEPA Formalism
This report presents a proposed formal approach towards reduction of sequences in PEPA components. By performing the described amalgamation procedure we may remove, from the Markov chain underlying an initial PEPA model, those states for which detailed local balance equations cannot be formulated. This transformation may lead to a simpler model with product form solution. Some classes of reduced models preserve those performance measures which we are interested in and, moreover, the steady state solution vector is much easier to find from the computational point of view
Fluid passage-time calculation in large Markov models
Recent developments in the analysis of large Markov models facilitate the fast approximation of transient characteristics of the underlying stochastic process. So-called fluid analysis makes it possible to consider previously intractable models whose underlying discrete state space grows exponentially as model components are added. In this work, we show how fluid approximation techniques may be used to extract passage-time measures from performance models. We focus on two types of passage measure: passage-times involving individual components; as well as passage-times which capture the time taken for a population of components to evolve. Specifically, we show that for models of sufficient scale, passage-time distributions can be well approximated by a deterministic fluid-derived passage-time measure. Where models are not of sufficient scale, we are able to generate approximate bounds for the entire cumulative distribution function of these passage-time random variables, using moment-based techniques. Finally, we show that for some passage-time measures involving individual components the cumulative distribution function can be directly approximated by fluid techniques
Extended Differential Aggregations in Process Algebra for Performance and Biology
We study aggregations for ordinary differential equations induced by fluid
semantics for Markovian process algebra which can capture the dynamics of
performance models and chemical reaction networks. Whilst previous work has
required perfect symmetry for exact aggregation, we present approximate fluid
lumpability, which makes nearby processes perfectly symmetric after a
perturbation of their parameters. We prove that small perturbations yield
nearby differential trajectories. Numerically, we show that many heterogeneous
processes can be aggregated with negligible errors.Comment: In Proceedings QAPL 2014, arXiv:1406.156
- ā¦