Parallel program design: a foundation
Parallel program design: a foundation
Temporal predicate transforms and fair termination
Acta Informatica
Probabilistic self-stabilization
Information Processing Letters
Probabilistic non-determinism
Programming from specifications (2nd ed.)
Programming from specifications (2nd ed.)
Probabilistic models for the guarded command language
Science of Computer Programming - Special issue: on formal specifications: foundations, methods, tools and applications: selected papers from the FMTA '95 conference (29–31 May 1995, Konstancin n. Warsaw, Poland)
Termination of Probabilistic Concurrent Program
ACM Transactions on Programming Languages and Systems (TOPLAS)
An axiomatic basis for computer programming
Communications of the ACM
A Discipline of Programming
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Partial correctness for probabilistic demonic programs
Theoretical Computer Science
A Formal Approach to Probabilistic Termination
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
Almost-certain eventualities and abstract probabilities in the quantitative temporal logic qTL
Theoretical Computer Science
Abstraction and refinement in probabilistic systems
ACM SIGMETRICS Performance Evaluation Review
Cost-based analysis of probabilistic programs mechanised in HOL
Nordic Journal of Computing
Probabilistic guarded commands mechanized in HOL
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
An elementary proof that Herman's ring is Θ(N2)
Information Processing Letters
Security, Probability and Nearly Fair Coins in the Cryptographers' Café
FM '09 Proceedings of the 2nd World Congress on Formal Methods
An elementary proof that Herman's Ring is Θ(N2)
Information Processing Letters
Probabilistic termination in B
ZB'03 Proceedings of the 3rd international conference on Formal specification and development in Z and B
Reasoning about a distributed probabilistic system
CATS '09 Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94
Linear-invariant generation for probabilistic programs: automated support for proof-based methods
SAS'10 Proceedings of the 17th international conference on Static 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
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Probabilistic predicate transformers provide a semantics for imperative programs containing both demonic and probabilistic nondeterminism. Like the (standard) predicate transformers popularised by Dijkstra, they model programs as functions from final results to the initial conditions sufficient to achieve them. This paper presents practical proof rules, using the probabilistic transformers, for reasoning about iterations when probability is present. They are thoroughly illustrated by example: probabilistic binary chop, faulty factorial, the martingale gambling strategy and Herman's probabilistic self-stabilisation. Just as for traditional programs, weakest-precondition based proof rules for program derivation are an important step on the way to designing more general refinement techniques, or even a refinement calculus, for imperative probabilistic programming.