Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
The Generalised Substitution Language Extended to Probabilistic Programs
B '98 Proceedings of the Second International B Conference on Recent Advances in the Development and Use of the B Method
SLIPE '85 Proceedings of the ACM SIGPLAN 85 symposium on Language issues in programming environments
Probabilistic guarded commands mechanized in HOL
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Security, Probability and Nearly Fair Coins in the Cryptographers' Café
FM '09 Proceedings of the 2nd World Congress on Formal Methods
Tank Monitoring: A pAMN Case Study
Electronic Notes in Theoretical Computer Science (ENTCS)
Qualitative probabilistic modelling in event-B
IFM'07 Proceedings of the 6th international conference on Integrated formal methods
YAGA: automated analysis of quantitative safety specifications in probabilistic B
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Development via refinement in probabilistic b: foundation and case study
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
Scaling probabilistic timing verification of hardware using abstractions in design source code
Proceedings of the International Conference on Formal Methods in Computer-Aided Design
Quantitative temporal logic mechanized in HOL
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
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Abrial's Generalised Substitution Language (GSL) [4] can be modified to operate on arithmetic expressions, rather than Boolean predicates, which allows it to be applied to probabilistic programs [13]. We add a new operator p⊕ to GSL, for probabilistic choice, and we get the probabilistic Generalised Substitution Language (pGSL): a smooth extension of GSL that includes random algorithms within its scope. In this paper we begin to examine the effect of pGSL on B's larger-scale structures: its machines. In particular, we suggest a notion of probabilistic machine invariant. We show how these invariants interact with pGSL, at a fine-grained level; and at the other extreme we investigate how they affect our general understanding "in the large" of probabilistic machines and their behaviour. Overall, we aim to initiate the development of probabilistic B (pB), complete with a suitable probabilistic AMN (pAMN). We discuss the practical extension of the B-Toolkit [5] to support pB, and we give examples to show how pAMN can be used to express and reason about probabilistic properties of a system.