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. The upper bound implies, for example, that each of the following tasks: renaming, order preserving renaming (Attiya et al, 1990) and binary monotone consensus (Biran et al., 1990) can be solved in the presence of one fault in 3 rounds of communications. All previous protocols that 1-solved these tasks required Ω(
doi:10.1016/0304-3975(95)00008-9 
Copyright © 1996 Published by Elsevier Science B.V.
About the p-paperfolding words
Communicated by D. Perrin
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Abstract
Let p be an integer greater than or equal to 2. The aim of this paper is to study the language associated to a p-paperfolding sequence. It is known that the number of factors of length n of a 2-paperfolding sequence (i.e. its complexity function) is P(n) = 4n for n 
7. It is also known that the language of all the factors of all 2-paperfolding sequences is not context-free and that its generating function is transcendental.
We show that the complexity function of a p-paperfolding sequence is either strictly subaffine or ultimately linear. The first case never happens if p = 2 or 3. In the second case, the complexity function is either P(n) = 2n or P(n) = 4n for n large enough. We give a simple necessary and sufficient condition for the number of special factors to be p-automatic. We finally show that, for any given p, the language of all factors of all p-paperfolding sequences is not context-free, and that the associated generating series is not algebraic.
