Formal Models of Communicating Systems

Languages, Automata, and Monadic Second-Order Logic

By: Benedikt Bollig

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eText | 8 September 2006

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This book studies the relationship between automata and monadic second-order logic, focusing on classes of automata that describe the concurrent behavior of distributed systems. It provides a unifying theory of communicating automata and their logical properties. Based on Hanf's Theorem and Thomas's graph acceptors, it develops a result that allows us to characterize many popular models of distributed computation in terms of the existential fragment of monadic second-order logic. In particular, the book covers finite automata, asynchronous (cellular) automata, communicating finite-state machines, and lossy channel systems. Model behavior is described using graphs and partial orders, leading to the notions of Mazurkiewicz traces, message sequence charts, and live sequence charts. This book is suitable for senior undergraduate and graduate courses on advanced automata theory, concurrency and communication issues. It can also be used as a reference by researchers concerned with the formal modeling of concurrent systems. Some knowledge of automata theory is a prerequisite. Numerous exercises, chapter summaries, and suggested reading allow for self-study, while the book is supported with a website containing course material and solutions.