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Turing Award-winner Leslie Lamport shares the key lessons he has learned about concurrent and distributed computing over decades of writing and reasoning about their algorithms. Algorithms are not programs, and they shouldn't be written in a programming language. Instead, this book explores how to write them and reason about them by using mathematics. It explains the principles underlying abstract programs, which should be implemented to avoid concurrency errors. Designing an abstract program before writing any code can lead to better, more reliable programs. The book has very few mathematical prerequisites, with an appendix summarizing the necessary knowledge. The examples are written in TLA+ and are available online. This is a fascinating read for any graduate students and researchers in theoretical computer science, concurrency, and distributed systems.
Computable structure theory quantifies and studies the relative complexity of mathematical structures. This text, in conjunction with the author's previous volume, represents the first full monograph on computable structure theory in two decades. It brings new results of the author together with many older results that were previously scattered across the literature and presents them all in a coherent framework. Geared towards graduate students and researchers in mathematical logic, the book enables the reader to learn all the main results and techniques in the area for application in their own research. While the previous volume focused on countable structures whose complexity can be measured within arithmetic, this second volume delves into structures beyond arithmetic, moving into the realm of the hyperarithmetic and the infinitary languages.