The interplay between words, computability, algebra and arithmetic
has now proved its relevance and fruitfulness. Indeed, the
cross-fertilization between formal logic and finite automata (such
as that initiated by J.R. Buchi) or between combinatorics on words
and number theory has paved the way to recent dramatic
developments, for example, the transcendence results for the real
numbers having a "simple" binary expansion, by B. Adamczewski and
Y. Bugeaud. This book is at the heart of this interplay through a
unified exposition. Objects are considered with a perspective that
comes both from theoretical computer science and mathematics.
Theoretical computer science offers here topics such as decision
problems and recognizability issues, whereas mathematics offers
concepts such as discrete dynamical systems. The main goal is to
give a quick access, for students and researchers in mathematics or
computer science, to actual research topics at the intersection
between automata and formal language theory, number theory and
combinatorics on words. The second of two volumes on this subject,
this book covers regular languages, numeration systems, formal
methods applied to decidability issues about infinite words and
sets of numbers.
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