Heterogeneous Formal specification of a Holonic MAS methodology based on Petri Nets and Object-Z Belhassen MAZIGH Faculty of sciences, Department of Computer Science, 5000, Monastir, Tunisia Email: belhassen.mazigh@gmail.com Mohamed GAROUI Faculty of sciences, Department of Computer Science, 5000, Monastir, Tunisia Email: garouimohamed2010@gmail.com Abderrafiaa KOUKAM University of Technology of Belfort Montbéliard, Belfort, France Email: abder.koukam@utbm.fr Abstract—The objective of this work is to formalize a Holonic methodology called ASPECS by using a formal specification approch based on two formalisms: Petri Net (PN) and Object-Z (OZ) language. Such a specification style facilitates the modeling of complex systems with both structural and behavioral aspects. Our generic approach is illustrated by applying it to FIRA Robot Soccer and it is validated with the SAL framework. Index Terms—Multi-Agents Systems, Formal Specification, Petri Nets, Object-Z, SAL. I. I NTRODUCTION I N COMPUTER science, a formal specification is a mathe- matical description of software or hardware that may be used to develop an implementation. It describes what the system should do but not (necessarily) how the system should proceed. Given such a specification, it is possible to use formal verification techniques to demonstrate that a candidate system design is correct with respect to the specification. This has the advantage that incorrect candidate system designs can be revised before a major investment has been made in actually implementing the design. An alternative approach is to use provably correct refinement steps to transform a specification into a design, and ultimately into an actual implementation that is correct by construction. A design (or implementation) can never be declared correct in isolation, but only “correct with respect to a given specifica- tion.” Whether the formal specification correctly describes the problem to be solved is a separate issue. It is also a difficult issue to address, since it ultimately concerns the problem constructing abstracted formal representations of an informal concrete problem domain, and such an abstraction step is not amenable to formal proof. However, it is possible to validate a specification by proving challenging theorems concerning properties that the specification is expected to exhibit. If correct, these theorems reinforce the specifier’s understanding of the specification and its relationship with the underlying problem domain. If not, the specification probably needs to be changed to better reflect the understanding domain of those involved in producing (and implementing) the specification. In specification domain, there are several methodologies to help modely and analyze Multi-Agents and Holonic systems. Among these methodologies, we point out the well known : Tropos [1], PASSI [2] and ASPECS [3, 6]. The objective of this work consists in consolidating an Agent-oriented Software Process for Engineering Complex Systems called ASPECS by using a formal specification and analysis and validate such a specification with the framework SAL (Symbolic Analysis Laboratory). After a brief presentation of the simulator for the FIRA Robot Soccer competition is presented, a quick overview of the ASPECS process and modelling approach will be presented in section 3. Section 4 present formal specifications of the various domains of ASPECS process based on composition of Petri Nets and Object-Z language named PNOZ. Section 5 present the validation process of PNOZ specification with the framework SAL. Finally, Section 6 summarises the results of the paper and describes some future work directions. II. CASE STUDY: FIRA ROBOT SOCCER This case study intends to model a simulator for the FIRA Robot Soccer competition [4]. This competition involves two teams of five autonomous robots playing a game similar to soccer (Fig.1). This is a classical example where real-time coordination is required. It constitutes a well-known benchmark for several research fields, such as Multi Agents Systems (MAS), image processing and control. Robot soccer players are two wheel driven small mobile robots, which are controlled by a host computer. A soccer team in the category of MiroSOT (Micro Robot World Cup Soccer Tournament) consists of five players, one goal keeper and four players for each team. There are several game categories. The size and form of the robot in each category is fixed by rules. Robot soccer competitions give an opportunity to foster intelligent techniques and intelligent robotics research by providing a standard problem where a wide spectrum of technologies can be developed, tested and integrated, e.g., collaborative multiple agent robotics, autonomous computing, Proceedings of the Federated Conference on Computer Science and Information Systems pp. 661–668 ISBN 978-83-60810-22-4 978-83-60810-39-2/$25.00 c  2011 IEEE 661