Numeration Systems: a Link between Number Theory and Formal Language Theory

Details Numeration Systems: a Link between Number Theory and Formal Language Theory Numeration Systems: a Link between Number Theory and Formal Language Theory

2012-04-26

arxiv.org/abs/1204.5887v1

Proceedings of Developments in Language Theory, London, Ontario, Canada (2010), Lect. Notes in Comput. Sci. 6224, 33-53 Spring

Computer Science

Formal Languages and Automata Theory

21 pages, 3 figures, invited talk DLT'2010

Scientific paper

We survey facts mostly emerging from the seminal results of Alan Cobham obtained in the late sixties and early seventies. We do not attempt to be exhaustive but try instead to give some personal interpretations and some research directions. We discuss the notion of numeration systems, recognizable sets of integers and automatic sequences. We briefly sketch some results about transcendence related to the representation of real numbers. We conclude with some applications to combinatorial game theory and verification of infinite-state systems and present a list of open problems.

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