Probabilistic predicate transformers
ACM Transactions on Programming Languages and Systems (TOPLAS)
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)
Probabilistic Simulations for Probabilistic Processes
CONCUR '94 Proceedings of the Concurrency Theory
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Abstraction, Refinement And Proof For Probabilistic Systems (Monographs in Computer Science)
Distributing probability over non-determinism
Mathematical Structures in Computer Science
Probability of Error in Information-Hiding Protocols
CSF '07 Proceedings of the 20th IEEE Computer Security Foundations Symposium
Semantic Domains for Combining Probability and Non-Determinism
Electronic Notes in Theoretical Computer Science (ENTCS)
The shadow knows: refinement of ignorance in sequential programs
MPC'06 Proceedings of the 8th international conference on Mathematics of Program Construction
Model checking hierarchical probabilistic systems
ICFEM'10 Proceedings of the 12th international conference on Formal engineering methods and software engineering
A UTP semantics of pGCL as a homogeneous relation
IFM'12 Proceedings of the 9th international conference on Integrated Formal Methods
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Early support for reasoning about probabilistic system behaviour replaced nondeterminism with probabilism. Only relatively recently have formalisms been studied that combine the two, and hence facilitate reasoning about probabilistic systems at levels of abstraction more general than code. Such studies have revealed an unsuspected subtlety in the interaction between nondeterministic and probabilistic choices that can be summarised: the demon resolving the nondeterministic choice has memory of previous state changes, whilst the probabilistic choice is made spontaneously. As a result, assignments to distinct variables need no longer commute. This paper introduces a model with explicit control of the length of the demon's memory. It does so by expanding the standard (initial-final) state view of computation to incorporate a third state, the `original' state which checkpoints the most recent nondeterministic choice. That enables a nondeterministic choice to be made on the basis of only certain past probabilistic choices and so facilitates independent nondeterministic combinations to be chosen against just those. Sound laws are presented and used to analyse first an example in which no new behaviour should result, and second one that lies beyond the scope of traditional models.