Performance queries on Semi-Markov Stochastic Petri nets with an extended continuous Stochastic logic

Semi-Markov Stochastic Petri Nets (SM-SPNs) are a highlevel formalism for defining semi-Markov processes. We present an extended Continuous Stochastic Logic (eCSL) which provides an expressive way to articulate performance queries at the SM-SPN model level. eCSL supports queries involving steady-state, transient and passage time measures. We demonstrate this by formulating and answering eCSL queries on an SM-SPN model of a distributed voting system with up to ¢¤£¦ ¥ states.

Petri nets for systems and synthetic biology

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which uni¯es the qualita- tive, stochastic and continuous paradigms. Each perspective adds its con- tribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how quali- tative descriptions are abstractions over stochastic or continuous descrip- tions, and show that the stochastic and continuous models approximate each other. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks

Derivation of passage-time densities in PEPA models using ipc: the imperial PEPA compiler

We present a technique for defining and extracting passage-time densities from high-level stochastic process algebra models. Our high-level formalism is PEPA, a popular Markovian process algebra for expressing compositional performance models. We introduce ipc, a tool which can process PEPA-specified passage-time densities and models by compiling the PEPA model and passage specification into the DNAmaca formalism. DNAmaca is an established modelling language for the low-level specification of very large Markov and semi-Markov chains. We provide performance results for ipc/DNAmaca and comparisons with another tool which supports PEPA, PRISM. Finally, we generate passage-time densities and quantiles for a case study of a high-availability web server. 1

Distributed computation of transient state distributions and passage time quantiles in large semi-Markov models

Submitted versio

Presentation of the 9th Edition of the Model Checking Contest.

International audience; The Model Checking Contest (MCC) is an annual competition of software tools for model checking. Tools must process an increasing benchmark gathered from the whole community and may participate in various examinations: state space generation, computation of global properties, computation of some upper bounds in the model, evaluation of reachability formulas, evaluation of CTL formulas, and evaluation of LTL formulas.For each examination and each model instance, participating tools are provided with up to 3600 s and 16 gigabyte of memory. Then, tool answers are analyzed and confronted to the results produced by other competing tools to detect diverging answers (which are quite rare at this stage of the competition, and lead to penalties).For each examination, golden, silver, and bronze medals are attributed to the three best tools. CPU usage and memory consumption are reported, which is also valuable information for tool developers

Comparative Analysis of Statistical Model Checking Tools

Statistical model checking is a powerful and flexible approach for formal verification of computational models like P systems, which can have very large search spaces. Various statistical model checking tools have been developed, but choosing between them and using the most appropriate one requires a significant degree of experience, not only because different tools have different modelling and property specification languages, but also because they may be designed to support only a certain subset of property types. Furthermore, their performance can vary depending on the property types and membrane systems being verified. In this paper we evaluate the performance of various common statistical model checkers against a pool of biological models. Our aim is to help users select the most suitable SMC tools from among the available options, by comparing their modelling and property specification languages, capabilities and performances

Probabilistic reasoning and inference for systems biology

One of the important challenges in Systems Biology is reasoning and performing hypotheses testing in uncertain conditions, when available knowledge may be incomplete and the experimental data may contain substantial noise. In this thesis we develop methods of probabilistic reasoning and inference that operate consistently within an environment of uncertain knowledge and data. Mechanistic mathematical models are used to describe hypotheses about biological systems. We consider both deductive model based reasoning and model inference from data. The main contributions are a novel modelling approach using continuous time Markov chains that enables deductive derivation of model behaviours and their properties, and the application of Bayesian inferential methods to solve the inverse problem of model inference and comparison, given uncertain knowledge and noisy data. In the first part of the thesis, we consider both individual and population based techniques for modelling biochemical pathways using continuous time Markov chains, and demonstrate why the latter is the most appropriate. We illustrate a new approach, based on symbolic intervals of concentrations, with an example portion of the ERK signalling pathway. We demonstrate that the resulting model approximates the same dynamic system as traditionally defined using ordinary differential equations. The advantage of the new approach is quantitative logical analysis; we formulate a number of biologically significant queries in the temporal logic CSL and use probabilistic symbolic model checking to investigate their veracity. In the second part of the thesis, we consider the inverse problem of model inference and testing of alternative hypotheses, when models are defined by non-linear ordinary differential equations and the experimental data is noisy and sparse. We compare and evaluate a number of statistical techniques, and implement an effective Bayesian inferential framework for systems biology based on Markov chain Monte Carlo methods and estimation of marginal likelihoods by annealing-melting integration. We illustrate the framework with two case studies, one of which involves an open problem concerning the mediation of ERK phosphorylation in the ERK pathway