Security, Probability and Nearly Fair Coins in the Cryptographers' Café
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Automating refinement checking in probabilistic system design
ICFEM'07 Proceedings of the formal engineering methods 9th international conference on Formal methods and software engineering
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The introduction of probabilistic behaviour into the B-method is a recent development. In addition to allowing probabilistic behaviour to be modelled, the relationship between expected values of the machine state can be expressed and verified. This paper explores the application of probabilistic B to a simple case study: tracking the volume of liquid held in a tank by measuring the flow of liquid into it. The flow can change as time progresses, and sensors are used to measure the flow with some degree of accuracy and reliability, modelled as non-deterministic and probabilistic behaviour respectively. At the specification level, the analysis is concerned with the expectation clause in the probabilistic B machine and its consistency with machine operations. At the refinement level, refinement and equivalence laws on probabilistic GSL are used to establish that a particular design of sensors delivers the required level of reliability.