What does a probabilistic program actually compute? How can one formally reason about such probabilistic programs? This valuable guide covers such elementary questions and more. It provides a state-of-the-art overview of the theoretical underpinnings of modern probabilistic programming and their applications in machine learning, security, and other domains, at a level suitable for graduate students and non-experts in the field. In addition, the book treats the connection between probabilistic programs and mathematical logic, security (what is the probability that software leaks confidential information?), and presents three programming languages for different applications: Excel tables, program testing, and approximate computing. This title is also available as Open Access on Cambridge Core.

Testing is the primary hardware and software verification technique used by industry today. Usually, it is ad hoc, error prone, and very expensive. In recent years, however, many attempts have been made to develop more sophisticated formal testing methods. This coherent book provides an in-depth assessment of this emerging field, focusing on formal testing of reactive systems.

This book is based on a seminar held in Dagstuhl Castle, Germany, in January 2004. It presents 19 carefully reviewed and revised lectures given at the seminar in a well-balanced way ensuring competent complementary coverage of all relevant aspects. An appendix provides a glossary for model-based testing and basics on finite state machines and on labelled transition systems. The lectures are presented in topical sections on testing of finite state machines, testing of labelled transition systems, model-based test case generation, tools and case studies, standardized test notation and execution architectures, and beyond testing.

It is with great pleasure that we present to you this tutorial volume entitled Validation of Stochastic Systems.ItisoneoftheresultsoftheDutch-German- lateral cooperation project "Validation of Stochastic Systems" (VOSS), ?nanced by NWO and DFG (the Dutch and German science foundations, respectively). In the early days of 2002, the idea emerged to organize a seminar at Schloss Dagstuhl, not the usual Dagstuhl seminar with primarily invited participants, but a seminar aimed at young(er) people, and for which the organizers assign themes to be worked upon and presented on. Following an open call announced via the Internet in the spring of 2002, we received many applications for part- ipation. After a selection procedure, we decided to assign (mostly) teams of two researchers to work on speci?c topics, roughly divided into the following four theme areas: "Modelling of Stochastic Systems," "Model Checking of Stochastic Systems," "Representing Large State Spaces," and "Deductive Veri?cation of Stochastic Systems." These are the titles of the four parts of this volume. TheseminarwasheldinSchlossDagstuhlduringDecember8-11,2002aspart of the so-called GI/Research Seminar series. This series of seminars is ?nancially supported by theGesellschaft fur ] Informatik, the German Computer Society. At that point in time the papers had already undergone a ?rst review round. Each of the tutorial papers was presented in a one-hour session, and on the basis of the presentations we decided to bring together a selection of them into a book."

This book constitutes the refereed proceedings of the 8th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2002, held in Grenoble, France, in April 2002.The 29 revised full papers presented together with one invited paper and four tool papers were carefully reviewed and selected from 95 submissions. The papers are organized in topical sections on real-time and probabilistic systems, scheduling, miscellaneous, software verification, infinite-state and parametric systems, model checking: logics and algorithms, model checking and testing, partial-order and simulation techniques, and debugging with model checking.

Traditionally, models and methods for the analysis of the functional correctness of reactive systems, and those for the analysis of their performance (and - pendability) aspects, have been studied by di?erent research communities. This has resulted in the development of successful, but distinct and largely unrelated modeling and analysis techniques for both domains. In many modern systems, however, the di?erence between their functional features and their performance properties has become blurred, as relevant functionalities become inextricably linked to performance aspects, e.g. isochronous data transfer for live video tra- mission. During the last decade, this trend has motivated an increased interest in c- bining insights and results from the ?eld of formal methods - traditionally - cused on functionality - with techniques for performance modeling and analysis. Prominent examples of this cross-fertilization are extensions of process algebra and Petri nets that allow for the automatic generation of performance models, the use of formal proof techniques to assess the correctness of randomized - gorithms, and extensions of model checking techniques to analyze performance requirements automatically. We believe that these developments markthe - ginning of a new paradigm for the modeling and analysis of systems in which qualitative and quantitative aspects are studied from an integrated perspective. We are convinced that the further worktowards the realization of this goal will be a growing source of inspiration and progress for both communities.

This book constitutes the proceedings of the 5th International Symposium on Dependable Software Engineering: Theories, Tools, and Applications, SETTA 2019, held in Shanghai, China, in November 2019. The 8 full papers presented were carefully reviewed and selected from 26 submissions. They present cutting-edge advancements in the field of formal methods and its interoperability with software engineering and focus on the application of formal techniques and tools for building reliable, safe, secure, and smart systems with multi-dimensional complexities.

This Festschrift volume has been published in honor of Ed Brinksma, on the occasion of his 60th birthday. The contributions in this Festschrift are written by a number of Ed's former Ph.D. students and collaborators. The papers are a reflection on his research contributions and interests and all fall into the area of formal methods, or in Ed's terminology applied mathematics in computer science. The papers address modeling languages and semantics, model-based testing, verification and performance analysis, probabilistic computation, system dynamics, and applications of formal methods.