Relatively Complete Verification of Probabilistic Programs: An Expressive Language for Expectation-Based Reasoning

We study a syntax for specifying quantitative “assertions” - functions mapping program states to numbers - for probabilistic program verification. We prove that our syntax is expressive in the following sense: Given any probabilistic program C, if a function f is expressible in our syntax, then the function mapping each initial state σ to the expected value of f evaluated in the final states reached after termination C on σ (also called the weakest preexpectation wp[C](f)) is also expressible in our syntax. As a consequence, we obtain a relatively complete verification system for verifying expected values and probabilities in the sense of Cook: Apart from a single reasoning step about the inequality of two functions given as syntactic expressions in our language, given f, g, and C, we can check whether g ≤ wp[C](f)

A Pre-expectation Calculus for Probabilistic Sensitivity

Sensitivity properties describe how changes to the input of a program affect the output, typically by upper bounding the distance between the outputs of two runs by a monotone function of the distance between the corresponding inputs. When programs are probabilistic, the distance between outputs is a distance between distributions. The Kantorovich lifting provides a general way of defining a distance between distributions by lifting the distance of the underlying sample space; by choosing an appropriate distance on the base space, one can recover other usual probabilistic distances, such as the Total Variation distance. We develop a relational pre-expectation calculus to upper bound the Kantorovich distance between two executions of a probabilistic program. We illustrate our methods by proving algorithmic stability of a machine learning algorithm, convergence of a reinforcement learning algorithm, and fast mixing for card shuffling algorithms. We also consider some extensions: using our calculus to show convergence of Markov chains to the uniform distribution over states and an asynchronous extension to reason about pairs of program executions with different control flow

Workshop: Schifffahrt und Logistik auf Binnenwasserstrassen - NAVILOG 2002 Tagungsband

SIGLEAvailable from TIB Hannover: ZA 2371(88) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Schnelle Binnenschiffe fuer Kombiverkehre und Containertransport. Konzepte und Techniken im Kuestenschutz im Land Niedersachsen. Grundlagen fuer den Aufbau verteilt agierender Umweltinformationssysteme

Available from TIB Hannover: ZA 2371(84); L bau820j / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Konstruktive Massnahmen zur Stabilisierung von Deichen. Simulation von Sedimenttransportprozessen in tidebeeinflussten Hafengebieten. Folgen von klimabedingten Wasserstands- und Windaenderungen fuer den Kuestenschutz an der Unterweser. Anwendbarkeit kommerzieller Radar-Wasserstandspegel zur Seegangsmessung

SIGLEAvailable from TIB Hannover: ZA 2371(86); L bau820j / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Feldprojekt Buerosystem Akzeptanzbedingungen und Einsatzfelder eines integrierten Buerosystems mit Spracheingabe

SIGLETIB: AC 9658 / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman