Customer Reviews

Automatic Sequences: Theory, Applications, Generalizations

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In 1983 Lothaire's "Combinatorics on Words" became the definitive resource on the area of stringology. 20 years later, Jean-Paul Allouche and Jeffrey Shallit's "Automatic Sequences" is set to be its heir. Pulling in countless concepts from many seemingly dissimilar disciplines, Allouche and Shallit are successful in bringing them together in an extremely informative and concise way. With detailed chapter notes and an immense bibliography the possible areas of exploration on each topic prove endless. A great resource for everyone from the serious researcher to the casually interested, this text is applicable to almost every area of mathematics and computer science. As the authors put it, "Sequences, both finite and infinite are ubiquitous in mathematics and theoretical computer science." If quality were synonymous popularity then this book will be equally ubiquitous.

I am enjoying this book immensely. It fills a real need in the literature of automatic sequences. The references and end notes at each chapter conclusion are very useful. Basically this book brings together a lot of disparate ideas and forms them into a coherent and well laid out presentation. My only reservation with the book is that there are minor errors with some of the proofs that can be annoying (but easily fixable). The style is accessible, the ideas are fast moving and the comprehensiveness of ideas and references is inspirational. Definitely worth purchasing.