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

Automating the transformation-based analysis of visual languages

The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-009-0114-yWe present a novel approach for the automatic generation of model-to-model transformations given a description of the operational semantics of the source language in the form of graph transformation rules. The approach is geared to the generation of transformations from Domain-Specific Visual Languages (DSVLs) into semantic domains with an explicit notion of transition, like for example Petri nets. The generated transformation is expressed in the form of operational triple graph grammar rules that transform the static information (initial model) and the dynamics (source rules and their execution control structure). We illustrate these techniques with a DSVL in the domain of production systems, for which we generate a transformation into Petri nets. We also tackle the description of timing aspects in graph transformation rules, and its analysis through their automatic translation into Time Petri netsWork sponsored by the Spanish Ministry of Science and Innovation, project METEORIC (TIN2008-02081/TIN) and by the Canadian Natural Sciences and Engineering Research Council (NSERC)

Hybrid Petri net model of a traffic intersection in an urban network

Control in urban traffic networks constitutes an important and challenging research topic nowadays. In the literature, a lot of work can be found devoted to improving the performance of the traffic flow in such systems, by means of controlling the red-to-green switching times of traffic signals. Different techniques have been proposed and commercially implemented, ranging from heuristic methods to model-based optimization. However, given the complexity of the dynamics and the scale of urban traffic networks, there is still a lot of scope for improvement. In this work, a new hybrid model for the traffic behavior at an intersection is introduced. It captures important aspects of the flow dynamics in urban networks. It is shown how this model can be used in order to obtain control strategies that improve the flow of traffic at intersections, leading to the future possibility of controlling several connected intersections in a distributed way

Formal Model Engineering for Embedded Systems Using Real-Time Maude

This paper motivates why Real-Time Maude should be well suited to provide a formal semantics and formal analysis capabilities to modeling languages for embedded systems. One can then use the code generation facilities of the tools for the modeling languages to automatically synthesize Real-Time Maude verification models from design models, enabling a formal model engineering process that combines the convenience of modeling using an informal but intuitive modeling language with formal verification. We give a brief overview six fairly different modeling formalisms for which Real-Time Maude has provided the formal semantics and (possibly) formal analysis. These models include behavioral subsets of the avionics modeling standard AADL, Ptolemy II discrete-event models, two EMF-based timed model transformation systems, and a modeling language for handset software.Comment: In Proceedings AMMSE 2011, arXiv:1106.596

Process algebra for performance evaluation

This paper surveys the theoretical developments in the field of stochastic process algebras, process algebras where action occurrences may be subject to a delay that is determined by a random variable. A huge class of resource-sharing systems – like large-scale computers, client–server architectures, networks – can accurately be described using such stochastic specification formalisms. The main emphasis of this paper is the treatment of operational semantics, notions of equivalence, and (sound and complete) axiomatisations of these equivalences for different types of Markovian process algebras, where delays are governed by exponential distributions. Starting from a simple actionless algebra for describing time-homogeneous continuous-time Markov chains, we consider the integration of actions and random delays both as a single entity (like in known Markovian process algebras like TIPP, PEPA and EMPA) and as separate entities (like in the timed process algebras timed CSP and TCCS). In total we consider four related calculi and investigate their relationship to existing Markovian process algebras. We also briefly indicate how one can profit from the separation of time and actions when incorporating more general, non-Markovian distributions