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

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Developments in Language Theory (DLT 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6224))

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Abstract

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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  1. Institut de Mathématiques, Université de Liège, Grande Traverse 12 (B 37), B-4000, Liège, Belgium

    Michel Rigo

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  1. Michel Rigo
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  1. Dept. of Computer Science, University of Western Ontario, N6A 5B7, London, ON, Canada

    Yuan Gao , Hanlin Lu , Shinnosuke Seki  & Sheng Yu , ,  & 

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Rigo, M. (2010). Numeration Systems: A Link between Number Theory and Formal Language Theory. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds) Developments in Language Theory. DLT 2010. Lecture Notes in Computer Science, vol 6224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14455-4_6

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