We present a framework for modelling and analysis of real-world business workflows. Business processes regularly form the basis for the design of software services, and frequently display complex stochastic behaviour. The accurate evaluation of their qualitative aspects can allow for determining bounds on resources consumed during execution of business processes. Accurate resource provisioning is often central to ensuring the safe execution of a process. We first introduce a formalised core subset of the Business Process Modelling and Notation (BPMN), which we extend with probabilistic and non-deterministic branching and reward annotations. We then develop an algorithm for the efficient translation of these models into the guarded command language used by the model checker PRISM, in turn enabling model checking of BPMN processes and allowing for the calculation of a wide range of quantitative properties of business processes including transient probabilities, timing, occurrence and ordering of events, and best-and worst-case scenarios. The developments presented are illustrated using an example from the health-care industry.

Abstract-This paper describes the T-Ruby system for designing VLSI circuits, starting from formal specifications in which they are described in terms of relational abstractions of their behaviour. The design process involves correctness-preserving transformations based on proved equivalences between relations, together with the addition of constr:sints. A class of implementable relations is defined. The tool enables such relations to be simulated or ti~anslated into a circuit description in VHDL. The de. '31 'g n process is illustrated by the derivation of a circuit for 2-dimensional convolution.

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. v vi PrefaceThe book has arisen from material used for teaching a course on Distributed Systems at the Technical University of Denmark. The exercises at the ends of Chapters 2 to 8 also originate in this course, either as weekly assignments or, in some cases, as examination questions. I hope you find them as interesting-and maybe even as challenging-as my students have done.This text was originally written for third or fourth year students in Computer Science or Electrical Engineering, and is intended to be suitable for most final-year undergraduate or postgraduate courses on advanced data communications or computer networks. The reader is expected to have a software background, in particular including a basic knowledge of functional programming and parallel programming, combined with some knowledge of computer systems architecture and data transmission. Knowledge of formal methods, for example based on languages such as VDM or Z, is not essential, but to get the most out of the book you should know about the sort of discrete mathematics which is used in computer science, and be aware of the basic concepts of mathematical proof.Many people deserve thanks for helping me in the task of preparing this text, and especially for reading and commenting on the various drafts which have seen the light of day. I would particularly like to thank my colleagues Hans-Henrik Løvengreen of this department, Arne Skou of Aalborg University, Klaus Hansen of the University of Copenhagen and Henrik Reif Andersen of the IT University in Copenhagen for their comments on important parts of the text. I also owe a great debt of thanks to my many students, who have been exposed to several provisional versions of this book, a fate which they have borne stoically. Their help in finding errors and pointing out the shakier parts of the presentation, where the arguments were weakest or the explanations most difficult to follow, has been invaluable.Finally, I would like to thank my wife Lisbeth and daughter Melissa for continuing to be so tolerant about having an author in the house. The competition for the PC at home has at times been intense -and they have been really sweet about letting me win. . . .

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