Abstraction, Refinement and Proof for Probabilistic Systems

This book integrates coverage of random/probabilistic algorithms, assertion-based program reasoning, and refinement programming models, providing a highly focused survey on probabilistic program semantics. It illustrates by example the typical steps necessary in computer science to build a mathematical model of any programming paradigm, addressing an essential foundation topic for modern sequential programming methodology.

This unique, example-driven monograph integrates coverage of random/probabilistic algorithms, assertion-based program reasoning, and refinement programming models, providing a focused survey on probabilistic program semantics Includes supplementary material: sn.pub/extras

Autorentext

Mário S. Alvim is assistant professor in the Computer Science Department of the Universidade Federal de Minas Gerais in Belo Horizonte. His current research interests include formal methods for security and pri­vacy, as well as applications of quantitative information flow to fields beyond security. Kostas Chatzikokolakis is associate professor at the University of Athens. He works on security and pri­vacy, in particular quantitative information flow, location privacy, and differential privacy. Annabelle McIver is professor in the Dept. of Computing at Macquarie University in Sydney. She works on mathematical techniques for the verification of probabilistic systems. Carroll Morgan is professor in the School of Engineering and Computer Science at the University of New South Wales, and is affiliated with the Trustworthy Systems Group of CSIRO's Data61. His current interests are quantitative information flow, program derivation (including security), and proved correctness of multi­core operating-system kernels. Catuscia Palamidessi is director of research at Inria Saclay. She is the leader of COMÈTE, a research team in the Inria and École Polytechnique shared lab. Her main research interests are quantitative information flow, privacy, and concurrency theory. Geoffrey Smith is professor in the School of Computing and Information Sciences of Florida International University in Miami. His current research interests include quantitative information flow and its applications to cryptography.

Klappentext

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 with increasing specialization: Part I treats probabilistic program logic, including many examples and case studies; Part II sets out the detailed semantics; and Part III applies the approach to advanced material on temporal calculi and two-player games.

Topics and features:

• Presents a general semantics for both probability and demonic nondeterminism, including abstraction and data refinement

• Introduces readers to the latest mathematical research in rigorous formalization of randomized (probabilistic) algorithms * Illustrates by example the steps necessary for building a conceptual model of probabilistic programming "paradigm"

• Considers results of a large and integrated research exercise (10 years and continuing) in the leading-edge area of "quantitative" program logics

• Includes helpful chapter-ending summaries, a comprehensive index, and an appendix that explores alternative approaches

This accessible, focused monograph,written by international authorities on probabilistic programming, develops an essential foundation topic for modern programming and systems development. Researchers, computer scientists, and advanced undergraduates and graduates studying programming or probabilistic systems will find the work an authoritative and essential resource text.

Inhalt
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.