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

Towards Formal Interaction-Based Models of Grid Computing Infrastructures

Grid computing (GC) systems are large-scale virtual machines, built upon a massive pool of resources (processing time, storage, software) that often span multiple distributed domains. Concurrent users interact with the grid by adding new tasks; the grid is expected to assign resources to tasks in a fair, trustworthy way. These distinctive features of GC systems make their specification and verification a challenging issue. Although prior works have proposed formal approaches to the specification of GC systems, a precise account of the interaction model which underlies resource sharing has not been yet proposed. In this paper, we describe ongoing work aimed at filling in this gap. Our approach relies on (higher-order) process calculi: these core languages for concurrency offer a compositional framework in which GC systems can be precisely described and potentially reasoned about.Comment: In Proceedings DCM 2013, arXiv:1403.768

Modelling Concurrency with Comtraces and Generalized Comtraces

Comtraces (combined traces) are extensions of Mazurkiewicz traces that can model the "not later than" relationship. In this paper, we first introduce the novel notion of generalized comtraces, extensions of comtraces that can additionally model the "non-simultaneously" relationship. Then we study some basic algebraic properties and canonical reprentations of comtraces and generalized comtraces. Finally we analyze the relationship between generalized comtraces and generalized stratified order structures. The major technical contribution of this paper is a proof showing that generalized comtraces can be represented by generalized stratified order structures.Comment: 49 page

Rigorous Design of Fault-Tolerant Transactions for Replicated Database Systems using Event B

System availability is improved by the replication of data objects in a distributed database system. However, during updates, the complexity of keeping replicas identical arises due to failures of sites and race conditions among conflicting transactions. Fault tolerance and reliability are key issues to be addressed in the design and architecture of these systems. Event B is a formal technique which provides a framework for developing mathematical models of distributed systems by rigorous description of the problem, gradually introducing solutions in refinement steps, and verification of solutions by discharge of proof obligations. In this paper, we present a formal development of a distributed system using Event B that ensures atomic commitment of distributed transactions consisting of communicating transaction components at participating sites. This formal approach carries the development of the system from an initial abstract specification of transactional updates on a one copy database to a detailed design containing replicated databases in refinement. Through refinement we verify that the design of the replicated database confirms to the one copy database abstraction