Team PARIS

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Inria / Raweb 2003
Project: PARIS

# Project : paris

## Section: New Results

### Advanced models for the Grid

Participants : Jean-Pierre Banâtre, Yann Radenac.

We are considering unconventional approaches for Grid programming and, more generally, for the programming of distributed applications.

It is well known that the task of programming is very difficult in general and even harder when the environment is distributed. As usual, the best way to proceed is by separation of concerns. Programs are first expressed in a model independent of any architecture, and then are refined taking into account the properties of the (distributed) environment. Several properties have to be taken into account, for example correctness, coordination/cooperation, mobility, load balancing, migration, efficiency, security, robustness, time, reliability, availability, computing/communication ratio, etc.

The models that we investigate are based on multisets. These models are often presented through metaphors which make understanding easier and may provide new sources of inspiration. One well known metaphor is the chemical one but other metaphors can also be considered such as biology (like cells or DNA), animal societies (like ants or bees colonies), etc.

Our present work relies on the chemical reaction paradigm and more precisely on the Gamma model of programming. Our recent contributions, carried out in close cooperation with Pascal Fradet, now at Inria Rhône-Alpes (Project-Team POP ART), include the extension of Gamma to higher-order and the generalization of multiplicity.

The extension of the basic Gamma model to a higher-order Gamma makes it possible to consider a Gamma program as a member of a multiset, thus eligible for reactions as any other element of the multiset. Such a facility will be used to express such properties as code mobility. We have called that model, the $\gamma$ -calculus. This research has allowed us to define a hierarchy of $\gamma$ -calculi, from the most basic one (multisets, basic $\gamma$ -expressions) to a very rich higher-order $\gamma$ -calculus, much richer than the original Gamma model. A paper [25] was presented at the Workshop on Membrane Computing 2003, and a full presentation of this work will be available as an Inria Research Report.

The generalization of multiplicity of multisets of the $\gamma$ -calculus opens new ways to express coordination. In particular, we are investigating multisets with infinite cardinality and multisets with a negative cardinality. From our first investigations, these properties may allow the expression of very original coordination schemes.

Apart from completing the above research activities, our perspectives concern coordinations in Grid applications and the definition of a chemical object model for Grids programming.