NDLI: Refinement Algebra with Explicit Probabilism

Content Provider	IEEE Xplore Digital Library
Author	Rabehaja, T.M. Sanders, J.W.
Copyright Year	2009
Abstract	Refinement algebra provides axioms for the stepwise removal of abstraction, in the form of demonic nondeterminism, in a first-order system that supports reasoning about loops. It has been extended by Solin and Meinecke to computations involving implicit probabilistic choices: demonic nondeterminism then satisfies weaker properties. In this paper their axiom system is extended to capture explicit probabilistic choices. The first form is an unquantified probabilistic choice; the second is a partial quantified probabilistic choice (from which the usual binary probabilistic choice can be recovered). The new refinement algebra is sound with respect to 1-bounded expectation transformers, the premier model of probabilistic computations, but also with respect to a new model introduced here to capture more directly partial quantified computations. In this setting a `normal form' result of Kozen is proved, replacing multiple loops with a single loop that does the same job; and the extent to which the two forms of loop have the same expected number of steps to termination is considered. Being entirely first-order, the new refinement algebra is targeted to automation.
Starting Page	63
Ending Page	70
File Size	352196
Page Count	8
File Format	PDF
ISBN	9780769537573
DOI	10.1109/TASE.2009.53
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-07-29
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Automation Algebra Computational modeling probability Kleene algebra loops probabilistic Transformers semantics refinement algebra Software engineering
Content Type	Text
Resource Type	Article

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