Abstraction, Refinement and Proof for Probabilistic Systems [Paperback]

Illustrates by example the typical steps necessary in computer science to build a mathematical model of any programming paradigm .

Presents results of a large and integrated body of research in the area of 'quantitative' program logics.

Probabilistic guarded commands and their refinement logic.- to pGCL: Its logic and its model.- Probabilistic loops: Invariants and variants.- Case studies in termination: Choice coordination, the dining philosophers, and the random walk.- Probabilistic data refinement: The steam boiler.- Semantic structures.- Theory for the demonic model.- The geometry of probabilistic programs.- Proved rules for probabilistic loops.- Infinite state spaces, angelic choice and the transformer hierarchy.- Advanced topics: Quantitative modal logic and game interpretations.- Quantitative temporal logic: An introduction.- The quantitative algebra of qTL.- The quantitative modal ?-calculus, and gambling games.

Probabilistic techniques are increasingly being employed in computer programs and systems because they can increase efficiency in sequential algorithms, enable otherwise nonfunctional distribution applications, and allow quantification of risk and safety in general. This makes operational models of how they work, and logics for reasoning about them, extremely important.

Abstraction, Refinement and Proof for Probabilistic Systems presents a rigorous approach to modeling and reasoning about computer systems that incorporate probability. Its foundations lie in traditional Boolean sequential-program logicbut its extension to numeric rather than merely true-or-false judgments takes it much further, into areas such as randomized algorithms, fault tolerance, and, in distributed systems, almost-certain symmetry breaking. The presentation begins with the familiar assertional style of program development and continues l£Ý