0000000000408861
AUTHOR
Marie-pierre Béal
showing 6 related works from this author
Presentations of constrained systems with unconstrained positions
2005
International audience; We give a polynomial-time construction of the set of sequences that satisfy a finite-memory constraint defined by a finite list of forbidden blocks, with a specified set of bit positions unconstrained. Such a construction can be used to build modulation/error-correction codes (ECC codes) like the ones defined by the Immink-Wijngaarden scheme in which certain bit positions are reserved for ECC parity. We give a lineartime construction of a finite-state presentation of a constrained system defined by a periodic list of forbidden blocks. These systems, called periodic-finite-type systems, were introduced by Moision and Siegel. Finally, we present a linear-time algorithm for con…
Coding Partitions: Regularity, Maximality and Global Ambiguity
2007
The canonical coding partition of a set of words is the finest partition such that the words contained in at least two factorizations of a same sequence belong to a same class. In the case the set is not uniquely decipherable, it partitions the set into one unambiguous class and other parts that localize the ambiguities in the factorizations of finite sequences. We firstly prove that the canonical coding partition of a regular set contains a finite number of regular classes. We give an algorithm for computing this partition. We then investigate maximality conditions in a coding partition and we prove, in the regular case, the equivalence between two different notions of maximality. As an ap…
Forbidden words in symbolic dynamics
2000
AbstractWe introduce an equivalence relation≃between functions from N to N. By describing a symbolic dynamical system in terms of forbidden words, we prove that the≃-equivalence class of the function that counts the minimal forbidden words of a system is a topological invariant of the system. We show that the new invariant is independent from previous ones, but it is not characteristic. In the case of sofic systems, we prove that the≃-equivalence of the corresponding functions is a decidable question. As a more special application, we show, by using the new invariant, that two systems associated to Sturmian words having “different slope” are not conjugate.
CODING PARTITIONS OF REGULAR SETS
2009
A coding partition of a set of words partitions this set into classes such that whenever a sequence, of minimal length, has two distinct factorizations, the words of these factorizations belong to the same class. The canonical coding partition is the finest coding partition that partitions the set of words in at most one unambiguous class and other classes that localize the ambiguities in the factorizations of finite sequences. We prove that the canonical coding partition of a regular set contains a finite number of regular classes and we give an algorithm for computing this partition. From this we derive a canonical decomposition of a regular monoid into a free product of finitely many re…
Minimal forbidden words and symbolic dynamics
1996
We introduce a new complexity measure of a factorial formal language L: the growth rate of the set of minimal forbidden words. We prove some combinatorial properties of minimal forbidden words. As main result we prove that the growth rate of the set of minimal forbidden words for L is a topological invariant of the dynamical system defined by L.
Minimal forbidden patterns of multi-dimensional shifts
2005
We study whether the entropy (or growth rate) of minimal forbidden patterns of symbolic dynamical shifts of dimension 2 or more, is a conjugacy invariant. We prove that the entropy of minimal forbidden patterns is a conjugacy invariant for uniformly semi-strongly irreducible shifts. We prove a weaker invariant in the general case.