Towards modular verification of pathways: fairness and assumptions

Modular verification is a technique used to face the state explosion problem often encountered in the verification of properties of complex systems such as concurrent interactive systems. The modular approach is based on the observation that properties of interest often concern a rather small portion of the system. As a consequence, reduced models can be constructed which approximate the overall system behaviour thus allowing more efficient verification. Biochemical pathways can be seen as complex concurrent interactive systems. Consequently, verification of their properties is often computationally very expensive and could take advantage of the modular approach. In this paper we report preliminary results on the development of a modular verification framework for biochemical pathways. We view biochemical pathways as concurrent systems of reactions competing for molecular resources. A modular verification technique could be based on reduced models containing only reactions involving molecular resources of interest. For a proper description of the system behaviour we argue that it is essential to consider a suitable notion of fairness, which is a well-established notion in concurrency theory but novel in the field of pathway modelling. We propose a modelling approach that includes fairness and we identify the assumptions under which verification of properties can be done in a modular way. We prove the correctness of the approach and demonstrate it on the model of the EGF receptor-induced MAP kinase cascade by Schoeberl et al.Comment: In Proceedings MeCBIC 2012, arXiv:1211.347

Projectable semantics for Statecharts

Abstract It has been proved that it is impossible to combine in one semantics for reactive systems the notions of modularity, causality and synchronous hypothesis. This limits bottom-up development of specifications. In this paper we introduce the notion of projectability, which is weaker than modularity, we define a non global consistent semantics for Statecharts that enforces projectability, causality and synchronous hypothesis, and we prove that no global consistent semantics for Statecharts can enforce these three notions

Two semantics for Timed Default Concurrent Constraint Programming

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Privacy in Real-Time Systems

Abstract We study the problem of privacy in the framework of Timed Automata. By distinguishing between secret and observable actions we formulate a property of no-privacy in terms of a property of the language accepted by a Timed Automaton, and we give an algorithm checking such property

Towards a P Systems Normal Form Preserving Step-by-step Behavior

Starting from a compositional operational semantics of transition P Systems we have previously defined, we face the problem of developing an axiomatization that is sound and complete with respect to some behavioural equivalence. To achieve this goal, we propose to transform the systems into a unique normal form which preserves the semantics. As a first step, we introduce axioms which allow the transformation of mem- brane structures with no dissolving rules into flat membranes. We discuss the problems which arise when dissolving rules are allowed and we suggest possible solutions. We leave as future work the further step that leads to the wanted normal form

P Systems with Endosomes

P Systems are computing devices inspired by the structure and the func- tioning of a living cell. A P System consists of a hierarchy of membranes, each of them containing a multiset of objects, a set of evolution rules, and possibly other membranes. Evolution rules are applied to the objects of the same membrane with maximal parallelism. In this paper we present an extension of P Systems, called P Systems with Endosomes (PE Systems), in which endosomes can be explicitly modeled. We show that PE Systems are universal even if only the simplest form of evolution rules is considered, and we give one application examples

On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems

Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind of differential equations in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. In the literature, delay stochastic simulation algorithms have been proposed. These algorithms follow a "delay as duration" approach, namely they are based on an interpretation of a delay as the elapsing time between the start and the termination of a chemical reaction. This interpretation is not suitable for some classes of biological systems in which species involved in a delayed interaction can be involved at the same time in other interactions. We show on a DDE model of tumor growth that the delay as duration approach for stochastic simulation is not precise, and we propose a simulation algorithm based on a ``purely delayed'' interpretation of delays which provides better results on the considered model