1. 28/Dec/2005 Linking the -calculus and B-Method Damien Karkinsky PhD Symposium IFM 2005 ¼

2.  Distributed Systems display: 1.high degree of component autonomy, 2.instantiation & state encapsulation, 3.dynamic reconfiguration.  The –calculus interaction model seen as suitable abstraction for such application domains.  The B-Method offers separation of concerns when describing state components and a tool.  Common semantics between the two might offer a powerful formal framework. Motivation

3.  Differences between the two methods are: 1.actions are non-atomic, operations are atomic, 2.  has operational semantics, B denotational semantics.  The conventional approach in the research field is to give B operational semantics by: 1.encoding each TERM of B with a TERM of  2.proving that the encoding is sound and complete with respect to D B using bi-simulation. Background

4.  If a common semantics exists how would the MACHINE construct behave in a system of agents?  We use B denotational semantics to derive a labelled transition system LTS M.  LTS M is then extended and a wrapper is provided enabling interaction with -agents.  The design of the wrapper: 1.provides machine instantiation, 2.separates operations into non-atomic actions. Methodology

5. Methodology (cont.)  In the case of machines without I/O & no guards y LTS M val1val2 P1P2 zop h ¤ i op INTER ( ¿ ) + LTS M ¼ z LTS M ………

6. Methodology (cont.) val1 ¼ P1 zop h ¤ i op INTER LTS M ¿ ­ ? val1 ¼ P1 LTS M

7. Example on o ® o ® on LTS M

8. Example (cont.)

9. Using the wrapper  The process can be used in a system of -agents. [[( BEGIN )]]h z i

10. A problem ( # ¿ ) + ( # ¿ ) + # cp ( z ) b = 2 f n ( C 0 )

11. Future Work  We are interested in investigating controlled interactions between -agents and machine instances.  Verification of divergence freedom properties 1.The full -calculus is too open, 2.Machine communication internalised, 3.Bi-simulation does not distinguish divergence.