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The Ring of kregular Sequences, II JeanPaul Allouche

Summary: The Ring of k­regular Sequences, II
Jean­Paul Allouche
Laboratoire de Recherche en Informatique
B“atiment 490
F­91405 Orsay Cedex France
Jeffrey Shallit 1
Department of Computer Science
University of Waterloo
Waterloo, Ontario, Canada N2L 3G1
In this paper, we continue our study of k­regular sequences begun in 1992. We prove
some new results, give many new examples from the literature, and state some open
Key words: k­regular sequences, finite automata
1 Introduction
A sequence (a(n)) n–0 over a finite alphabet \Delta is said to be k­automatic if
there exists a finite automaton with output M = (Q; \Sigma k ; ffi; q 0 ; \Delta; ř ) such that
a(n) = ř (ffi(q 0 ; (n) k )) for all n – 0. Here
ffl Q is a finite nonempty set of states;


Source: Allouche, Jean-Paul - Laboratoire de Recherche en Informatique, Université de Paris-Sud 11


Collections: Computer Technologies and Information Sciences