Results 11 to 20 of about 144,803 (288)
Hidden automatic sequences [PDF]
Combinatorial Theory, 2021 An automatic sequence is a letter-to-letter coding of a fixed point of a uniform morphism. More generally, we have morphic sequences, which are letter-to-letter codings of fixed points of arbitrary morphisms. There are many examples where an, a priori, morphic sequence with a \emph{non-uniform} morphism happens to be an automatic sequence.
Allouche, Jean-Paul +2 more
openaire +7 more sources
On asymptotically automatic sequences
Acta ArithmeticaWe study the notion of an asymptotically automatic sequence, which generalises the notion of an automatic sequence. While $k$-automatic sequences are characterised by finiteness of $k$-kernels, the $k$-kernels of asymptotically $k$-automatic sequences are only required to be finite up to equality almost everywhere. We prove basic closure properties and
Konieczny, Jakub
core +5 more sources
On the Final Coalgebra of Automatic Sequences [PDF]
, 2012 Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences form a particularly interesting class of streams that live in both worlds at the same time: they are defined in terms of finite automata, which are basic computational structures in computer science; and they appear in mathematics in many different ways ...
Clemens Kupke, Jan J. M. M. Rutten
openaire +5 more sources
Averages of automatic sequences
Theoretical Computer Science, 2006 The authors are interested in the existence and computation of average and correlation function of (generalized) automatic sequences. They, in particular, give a precise sufficient condition for the existence of such means. This paper supersedes (part of) previous papers of the authors [J. Phys. A, Math. Gen. 38, No.
André Barbé, Fritz von Haeseler
openaire +2 more sources
, 2003 Automatic sequences are sequences which are produced by a finite automaton. Although they are not random they may look as being random. They are complicated, in the sense of not being not ultimately periodic, they may look rather complicated, in the ...
Jean-Paul Allouche, Jeffrey O. Shallit
core +4 more sources
Automatic Sequences and Zip-Specifications [PDF]
2012 27th Annual IEEE Symposium on Logic in Computer Science, 2012 We consider infinite sequences of symbols, also known as streams, and the decidability question for equality of streams defined in a restricted format. This restricted format consists of prefixing a symbol at the head of a stream, of the stream function `zip', and recursion variables.
Clemens Grabmayer +4 more
openaire +6 more sources
More on Generalized Automatic Sequences
J. Autom. Lang. Comb., 2002 Journal of Automata, Languages and Combinatorics, Volume 7, Number 3, 2002, 351 ...
Rigo, Michel, Maes, Arnaud
openaire +4 more sources
ENUMERATION AND DECIDABLE PROPERTIES OF AUTOMATIC SEQUENCES [PDF]
International Journal of Foundations of Computer Science, 2011 We show that various aspects of k-automatic sequences — such as having an unbordered factor of length n — are both decidable and effectively enumerable. As a consequence it follows that many related sequences are either k-automatic or k-regular. These include many sequences previously studied in the literature, such as the recurrence function, the ...
Charlier, Emilie +2 more
openaire +6 more sources
The Critical Exponent is Computable for Automatic Sequences [PDF]
Electronic Proceedings in Theoretical Computer Science, 2011 The critical exponent of an infinite word is defined to be the supremum of the exponent of each of its factors. For k-automatic sequences, we show that this critical exponent is always either a rational number or infinite, and its value is computable ...
Jeffrey Shallit
doaj +5 more sources
Complexity of Automatic Sequences [PDF]
Language and Automata Theory and Applications14th International Conference, 2020 Automatic sequences can be defined by DFAs with output (DFAO) in two natural ways. We propose to consider the minimal size of a corresponding DFAO as the complexity measure of the automatic sequence, for both variants. This paper compares these complexity measures and investigates their properties like the relationships with kernel and morphic ...
Zantema H.
europepmc +4 more sources