Download Abstraction, Refinement and Proof for Probabilistic Systems by Annabelle McIver PDF

By Annabelle McIver

Probabilistic suggestions are more and more being hired in desktop courses and platforms simply because they could raise potency in sequential algorithms, let in a different way nonfunctional distribution functions, and make allowance quantification of probability and safeguard as a rule. This makes operational versions of the way they paintings, and logics for reasoning approximately them, tremendous important.

Abstraction, Refinement and facts for Probabilistic Systems offers a rigorous method of modeling and reasoning approximately desktops that contain chance. Its foundations lie in conventional Boolean sequential-program logic—but its extension to numeric instead of only true-or-false judgments takes it a lot extra, into components equivalent to randomized algorithms, fault tolerance, and, in allotted platforms, almost-certain symmetry breaking. The presentation starts off with the commonplace "assertional" sort of software improvement and keeps with expanding specialization: half I treats probabilistic software common sense, together with many examples and case experiences; half II units out the precise semantics; and half III applies the method of complex fabric on temporal calculi and two-player games.

Topics and features:

* offers a normal semantics for either chance and demonic nondeterminism, together with abstraction and knowledge refinement

* Introduces readers to the newest mathematical examine in rigorous formalization of randomized (probabilistic) algorithms * Illustrates via instance the stairs beneficial for development a conceptual version of probabilistic programming "paradigm"

* Considers result of a wide and built-in study workout (10 years and carrying on with) within the modern sector of "quantitative" application logics

* contains useful chapter-ending summaries, a complete index, and an appendix that explores replacement approaches

This available, targeted monograph, written by means of overseas gurus on probabilistic programming, develops a necessary origin subject for contemporary programming and platforms improvement. Researchers, laptop scientists, and complex undergraduates and graduates learning programming or probabilistic platforms will locate the paintings an authoritative and crucial source text.

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Extra info for Abstraction, Refinement and Proof for Probabilistic Systems

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That if applied to a feasible transformer it returns a feasible transformer again. “Feasibility” of transformers is one of the “healthiness conditions” we will encounter in Sec. 6. For convenience, we usually assume that cntx is continuous as well. See Lem. 8 on p. 148. 5. Basic syntax and semantics of pGCL 27 choice, which corresponds to our intuition. 41 Finally, recursive programs have least-fixed-point semantics as usual. 6 Example of semantics: Monty Hall again We illustrate the semantics by returning to the program of Fig.

Sequential composition is functional composition. The semantics of demonic choice reflects the dual metaphors for it: as abstraction, we must take the minimum because we are giving a guarantee over all possible implementations; as a demon’s behaviour, we assume he acts to make our expected winnings as small as possible. The pre-expectation of probabilistic choice is the weighted average of the pre-expectations of its branches. e. that if applied to a feasible transformer it returns a feasible transformer again.

Introduction to pGCL 0 1 2 4 3 5 6 To play from a square, you first pick one of the face-down cards. ) Then you roll a die to choose one of the alternatives on the card. e. ) As special cases, a standard step (non-probabilistic) has only one alternative per card, but possibly many cards; and a deterministic step has only one card, but possibly many alternatives on it. A standard and deterministic step has one card, and only one alternative. The winning final positions — the postcondition — are the states {4, 5}, marked with a £1 coin.

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