ACM Transactions on Programming Languages and Systems (TOPLAS)
A generalization of Dijkstra's calculus
ACM Transactions on Programming Languages and Systems (TOPLAS)
Reasoning about probabilistic parallel programs
ACM Transactions on Programming Languages and Systems (TOPLAS)
Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
The B-book: assigning programs to meanings
The B-book: assigning programs to meanings
Termination of Probabilistic Concurrent Program
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Discipline of Programming
On the Refinement Calculus
A Formal Approach to Probabilistic Termination
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
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
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Proof rules for probabilistic loops
FAC-RW'96 Proceedings of the BCS-FACS 7th conference on Refinement
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
Probabilistic choice, reversibility, loops, and miracles
UTP'10 Proceedings of the Third international conference on Unifying theories of programming
Refinement-based verification of local synchronization algorithms
FM'11 Proceedings of the 17th international conference on Formal methods
The challenge of probabilistic event B
ZB'05 Proceedings of the 4th international conference on Formal Specification and Development in Z and B
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
Quantitative temporal logic mechanized in HOL
ICTAC'05 Proceedings of the Second international conference on Theoretical Aspects of Computing
Proving termination of probabilistic programs using patterns
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Reasoning about almost-certain convergence properties using Event-B
Science of Computer Programming
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The B Method [1] does not currently handle probability. We add it in a limited form, concentrating on "almost-certain" properties which hold with probability one; and we address briefly the implied modifications to the programs that support B. The Generalised Substitution Language is extended with a binary operator ⊕ representing "abstract probabilistic choice", so that the substitution prog1 ⊕ prog2 means roughly "choose between prog1 and prog2 with some probability neither one nor zero". We then adjust B's proof rule for loops -- specifically, the variant rule -- so that in many cases it is possible to prove "probability-one" correctness of programs containing the new operator, which was not possible in B before, while remaining almost entirely within the original Boolean logic. Applications include probabilistic algorithms such as the IEEE 1394 Root Contention Protocol ("FireWire") [9] in which a probabilistic "symmetry-breaking" strategy forms a key component of the design.