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sections on consensus and on causality and time are both pitched at an appropriate level for advanced undergraduates. The second section of the book concerns how to simulate one kind of system with another. This section starts by introducing some formal machinery, and proceeds to consider how to implement broadcast and multicast, correctness conditions for shared memory, implementations of read/write variables, and "compiling" algorithms designed to tolerate one kind of failure into algorithms that tolerate other kinds of failures. I covered the multicast algorithms and correctness conditions. Because of the emphasis on formalism, and the focus on subtle distinctions among failure models, the remaining material struck me as perhaps more appropriate for first-year graduate students. The third and final section of the book covers advanced topics. Students reacted well to the section on wait-fTee simulation of arbitrary objects (many were excited by applications to concurrent data structures), and to the section on asynchronously solvable systems. The section on random-ization interested students with a sllmciently strong background in probability theory. Problems such as bounded timestamping elicited less enthusiasm. The book includes a nllmber of exercises, which were quite useful in preparing homeworks and exams. Many of the exercises have bugs, however, so it is prudent to consult the authors' errata page at before making assignments. It should be mentioned that this text is about fundamentals of distributed computin9, not distributed aystema. It does not cover deadlock detection, two-phase locking and serializabflity theory, distributed commitment protocols, checkpointing, practical mutual exclusion algorithms, and other theoretical topics related to distributed systems. One mild criticism of the presentation is that the authors provide little or no explicit motivation for the models and problems considered in the text. In particular, the authors draw no distinction between problems interesting primariiy as mathematical exercises, and problems interesting because they tell us something about computation as it is practiced. To pick one example, when I taught the course, I felt it important to warn students that the problem of mutual exclusion using read-write variables is a valuable theoretical exercise, training them to think rigorously about concurrency, fairness properties, and so on, but that there are fundA.mental architectural reasons (which every computer scientist should understand) why it makes no sense to use read-write variables for mutual exclusion in real systems. By contrast, lower bounds such as the impossibility of fault-tolerant consensus in asynchronous systems do have wide-ranging applications for real …

Review of Hilbert's Tenth Problem by Yttri Matiyasevich