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Reviewer: Francois Aribaud

Academic Press has reprinted the famous Formal Languages by Arto Salomaa in its series of Computer Science Classics. There is no change from the first edition, which appeared in 1973. [ Ed. Note: See 15, 2 (Feb. 1974), Rev. 26,421.] Although the book is fifteen years old, it remains a masterpiece, of great value for every lecturer in language theory at the graduate level. Why has the publisher not appended an updating notice__ __ A Guide to the Literature in a book printed in 1987 with no references after 1972 cannot be taken seriously. There is a risk that Formal Languages will be treated merely as a venerable artifact from the good old days of Computer Science. That would be a pity. This book emphasizes the mathematical aspects of the subject from the viewpoint of generative devices. Grammars are the basic tools, but recognition devices are included. (In a fascinating, later book, Salomaa adopted the opposite scheme [1].) The first part of the book presents a rigorous analysis of the Chomsky hierarchy. Among the more specialized topics are :9Bthe study of regular and boolean operations in families of languages, the analysis of ambiguity and the introduction of LR( k) and LL( k) grammars, and the delicate balance between a rigorous mathematical treatment and the avoidance of the formidable apparatus of recursive functions in the treatment of solvability and unsolvability for context-free languages. In a course on language theory at the graduate level today, one must deal with complexity theory and especially with complexity hierarchies [2]. Unfortunately, this book omits the P/NP question, which had just emerged when the book was written. Although Formal Languages is no longer the leading book on language theory, it remains a basic reference.