Moving from Event-B to probabilistic Event-B

We propose a fully probabilistic extension of Event-B where all the non-deterministic choices are replaced with probabilities. We present the syntax and the semantics of this extension and introduce novel and adapted proof obligations for proving the correctness of probabilistic Event-B models. As a preliminary step towards handling refinement of probabilistic Event-B models, we propose sufficient conditions for the almost-certain convergence of a set of events and express them in terms of proof obligations. We illustrate our work by presenting a case study specified in both standard and probabilistic Event-B.

[1]  Dominique Cansell,et al.  Refinement and Reachability in EventB , 2005, ZB.

[2]  Jean-Raymond Abrial,et al.  Modeling in event-b - system and software engineering by Jean-Raymond Abrial , 2010, SOEN.

[3]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[4]  Elena Troubitsyna,et al.  Integrating stochastic reasoning into Event-B development , 2014, Formal Aspects of Computing.

[5]  Carroll Morgan,et al.  The Challenge of Probabilistic Event B - Extended Abstract , 2005, ZB.

[6]  Annabelle McIver,et al.  Abstraction, Refinement and Proof for Probabilistic Systems , 2004, Monographs in Computer Science.

[7]  Annabelle McIver,et al.  Probabilistic Invariants for Probabilistic Machines , 2003, ZB.

[8]  Burak Acar,et al.  Reliability, Availability, Maintainability and Safety Assessment in the Maritime Industry , 2017 .

[9]  Kishor S. Trivedi,et al.  Recent advances in modeling response-time distributions in real-time systems , 2003, Proc. IEEE.

[10]  G. Bolton.  Reliability , 2003, Medical Humanities.

[11]  Thai Son Hoang,et al.  Reasoning about almost-certain convergence properties using Event-B , 2014, Sci. Comput. Program..

[12]  Annabelle McIver,et al.  Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science) , 2004 .

[13]  Annabelle McIver,et al.  Development via Refinement in Probabilistic B - Foundation and Case Study , 2005, ZB.

[14]  Parosh Aziz Abdulla,et al.  Decisive Markov Chains , 2007, Log. Methods Comput. Sci..

[15]  Thai Son Hoang,et al.  Reasoning about Liveness Properties in Event-B , 2011, ICFEM.

[16]  Elena Troubitsyna,et al.  Towards Probabilistic Modelling in Event-B , 2010, IFM.

[17]  Dominique Cansell,et al.  A Mechanically Proved and Incremental Development of IEEE 1394 Tree Identify Protocol , 2003, Formal Aspects of Computing.

[18]  Thai Son Hoang,et al.  Qualitative Probabilistic Modelling in Event-B , 2007, IFM.

[19]  Wesley W. Chu,et al.  Estimating task response time with contentions for real-time distributed systems , 1988, Proceedings. Real-Time Systems Symposium.

[20]  Michael J. Butler,et al.  Practical Theory Extension in Event-B , 2013, Theories of Programming and Formal Methods.

[21]  Didier Bert,et al.  Construction of Finite Labelled Transistion Systems from B Abstract Systems , 2000, IFM.

[22]  Thai Son Hoang,et al.  Rodin: an open toolset for modelling and reasoning in Event-B , 2010, International Journal on Software Tools for Technology Transfer.

[23]  Annabelle McIver,et al.  Probabilistic Termination in B , 2003, ZB.

[24]  Elena Troubitsyna,et al.  Reliability Assessment in Event-B Development , 2009 .

[25]  Emre Yilmaz.  Tool support for qualitative reasoning in event-B , 2010 .