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DLT
2008
13 years 6 months ago
The Average State Complexity of the Star of a Finite Set of Words Is Linear
We prove that, for the uniform distribution over all sets X of m (that is a fixed integer) non-empty words whose sum of lengths is n, DX , one of the usual deterministic automata r...
Frédérique Bassino, Laura Giambruno,...
DLT
2008
13 years 6 months ago
Fixed Point and Aperiodic Tilings
An aperiodic tile set was first constructed by R. Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics rangin...
Bruno Durand, Andrei E. Romashchenko, Alexander Sh...
DLT
2008
13 years 6 months ago
Universal Recursively Enumerable Sets of Strings
The present work clarifies the relation between domains of universal machines and r.e. prefix-free supersets of such sets. One such characterisation can be obtained in terms of the...
Cristian S. Calude, André Nies, Ludwig Stai...
DLT
2008
13 years 6 months ago
Relationally Periodic Sequences and Subword Complexity
By the famous theorem of Morse and Hedlund, a word is ultimately periodic if and only if it has bounded subword complexity, i.e., for sufficiently large n, the number of factors of...
Julien Cassaigne, Tomi Kärki, Luca Q. Zamboni
DLT
2008
13 years 6 months ago
Hierarchies of Piecewise Testable Languages
The classes of languages which are boolean combinations of languages of the form A a1A a2A . . . A a A , where a1, . . . , a A, k , for a fixed k 0, form a natural hierarchy wit...
Ondrej Klíma, Libor Polák
DLT
2008
13 years 6 months ago
Algorithmically Independent Sequences
Cristian S. Calude, Marius Zimand