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Abstraction, Refinement and Proof for Probabilistic Systems - download pdf or read online

By Annabelle McIver

ISBN-10: 0387401156

ISBN-13: 9780387401157

Probabilistic suggestions are more and more being hired in laptop courses and structures simply because they could bring up potency in sequential algorithms, permit in a different way nonfunctional distribution purposes, and make allowance quantification of danger and defense typically. This makes operational versions of ways they paintings, and logics for reasoning approximately them, super important.

Abstraction, Refinement and evidence for Probabilistic Systems provides a rigorous method of modeling and reasoning approximately desktops that comprise likelihood. Its foundations lie in conventional Boolean sequential-program logic—but its extension to numeric instead of purely true-or-false judgments takes it a lot additional, into components corresponding to randomized algorithms, fault tolerance, and, in allotted platforms, almost-certain symmetry breaking. The presentation starts with the prevalent "assertional" sort of software improvement and maintains with expanding specialization: half I treats probabilistic application common sense, together with many examples and case stories; half II units out the particular semantics; and half III applies the method of complex fabric on temporal calculi and two-player games.

Topics and features:

* offers a common semantics for either likelihood and demonic nondeterminism, together with abstraction and knowledge refinement

* Introduces readers to the most recent mathematical study in rigorous formalization of randomized (probabilistic) algorithms * Illustrates through 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 region of "quantitative" software logics

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

This obtainable, concentrated monograph, written by means of foreign specialists on probabilistic programming, develops a necessary starting place subject for contemporary programming and platforms improvement. Researchers, desktop 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 resources for Abstraction, Refinement and Proof for Probabilistic Systems

Sample text

1, that it is not sound to consider only post-expectations postE of the form [post ] in Def. 1: it is necessary for refinement, but not sufficient, that prog be at least as likely to establish any postcondition post as prog is. 3. An informal computational model for pGCL = 3 5 ⊕ (x: = −y (x: = −y x: = −y x: = −y = 1 3 3 4 ⊕ ⊕ ⊕ 3⊕ 4 1 3 x: = +y) x: = +y) 11 Sec. 9) . 3 An informal computational model: pGCL describes gambling We now use a simple card-and-dice game as an informal introduction to the computational model for pGCL, to support the intuition for probabilistic choice, demonic choice and their interaction.

This definition is one of the main features of this approach. postE2 . And clearly non-negativity continues to hold. The characterisations of expectations given above for the simpler cases might suggest that non-negative and sublinear functionals uniquely determine a set of probability distributions — and, in Chap. 1 Syntax Let prog range over programs and p over real number expressions taking values between zero and one inclusive; assume that x stands for a list of distinct variables, and expr for a list of expressions (of the same length as x 24 She was working in a much more general context.

Prog are then of type TS. The expression-based view is more convenient in an introduction, and for the treatment of specific programs; the function-based view is more convenient (and, for recursion, necessary) for general properties of expectation transformers. In this chapter and the rest of Part I we retain the 38 A partial order differs from the familiar “total” orders like “≤” in that two elements can be “incomparable”; the most common example is subset ⊆ between sets, which satisfies reflexivity (a set is a subset of itself), anti-symmetry (two sets cannot be subsets of each other without being the same set) and transitivity (one set within a second within a third is a subset of the third directly as well).

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Abstraction, Refinement and Proof for Probabilistic Systems by Annabelle McIver


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