164,460 research outputs found
On the Growth Rates of Complexity of Threshold Languages
Threshold languages, which are the (k/(k-1))+-free languages over k-letter alphabets with k ≥, are the minimal infinite power-free languages according to Dejean's conjecture, which is now proved for all alphabets. We study the growth properties of these languages. On the base of obtained structural properties and computer-assisted studies we conjecture that the growth rate of complexity of the threshold language over k letters tends to a constant α̌ ≈ 1.242 as k tends to infinity. © 2010 EDP Sciences.The authors heartly thank the referees for their valuable comments and remarks
Geodesic growth in virtually abelian groups
We show that the geodesic growth function of any finitely generated virtually
abelian group is either polynomial or exponential; and that the geodesic growth
series is holonomic, and rational in the polynomial growth case. In addition,
we show that the language of geodesics is blind multicounter.Comment: 23 pages, 1 figure, improved readabilit
Binary Patterns in Binary Cube-Free Words: Avoidability and Growth
The avoidability of binary patterns by binary cube-free words is investigated
and the exact bound between unavoidable and avoidable patterns is found. All
avoidable patterns are shown to be D0L-avoidable. For avoidable patterns, the
growth rates of the avoiding languages are studied. All such languages, except
for the overlap-free language, are proved to have exponential growth. The exact
growth rates of languages avoiding minimal avoidable patterns are approximated
through computer-assisted upper bounds. Finally, a new example of a
pattern-avoiding language of polynomial growth is given.Comment: 18 pages, 2 tables; submitted to RAIRO TIA (Special issue of Mons
Days 2012
On the Commutative Equivalence of Context-Free Languages
The problem of the commutative equivalence of context-free and regular languages is studied. In particular conditions ensuring that a context-free language of exponential growth is commutatively equivalent with a regular language are investigated
On groups and counter automata
We study finitely generated groups whose word problems are accepted by
counter automata. We show that a group has word problem accepted by a blind
n-counter automaton in the sense of Greibach if and only if it is virtually
free abelian of rank n; this result, which answers a question of Gilman, is in
a very precise sense an abelian analogue of the Muller-Schupp theorem. More
generally, if G is a virtually abelian group then every group with word problem
recognised by a G-automaton is virtually abelian with growth class bounded
above by the growth class of G. We consider also other types of counter
automata.Comment: 18 page
Wikipedias: Collaborative web-based encyclopedias as complex networks
Wikipedia is a popular web-based encyclopedia edited freely and
collaboratively by its users. In this paper we present an analysis of
Wikipedias in several languages as complex networks. The hyperlinks pointing
from one Wikipedia article to another are treated as directed links while the
articles represent the nodes of the network. We show that many network
characteristics are common to different language versions of Wikipedia, such as
their degree distributions, growth, topology, reciprocity, clustering,
assortativity, path lengths and triad significance profiles. These
regularities, found in the ensemble of Wikipedias in different languages and of
different sizes, point to the existence of a unique growth process. We also
compare Wikipedias to other previously studied networks.Comment: v3: 9 pages, 12 figures, Change of title, few paragraphs and two
figures. Accepted for publication in Phys. Rev.
- …