PROVILLARD , Julien

This thesis introduces a new dynamical system which generalizes the cellular automata (CA) : non-uniform cellular automata (nuCA). The nuCAs are obtained by relaxing the spatial uniformity of the local rule of CAs. The global rule is now given by a distribution of local rules. Several classes of nuCAs are defined with respect to restrictions on...

The paper deals with recent developments about non-uniform cellular automata. After reviewing known results about structural stability we complete them by showing that also sensitivity to initial conditions is not structurally stable. The second part of the paper reports the complexity results about the main dy-namical properties. Some proofs...

This paper investigates a variant of cellular automata, namely ν-CA. Indeed, ν-CA are cellular automata which can have dierent local rules at each site of their lattice. The assignment of local rules to sites of the lattice completely characterizes ν-CA. In this paper, sets of assignments sharing some interesting properties are associated with...

A finite language X over an alphabet Σ is complete if any word in Σ* is a factor of a word in X*. A word which is not a factor of X* is said uncompletable. Among them, some are minimal as all their proper factors belong to Fact(X*). The problem is to find bounds on the length of the shortest minimal uncompletable words depending on k, the...

The dynamical behavior of non-uniform cellular automata is compared with the one of classical cellular automata. Several differences and similarities are pointed out by a series of examples. Decidability of basic properties like surjec-tivity and injectivity is also established. The final part studies a strong form of equicontinuity property...

This paper investigates acceptance conditions for nite au-tomata recognizing ω-regular languages. Their expressive power and their position w.r.t. the Borel hierarchy is also studied. The full characterization for the conditions (ninf,), (ninf, ⊆) and (ninf, =) is given. The nal section provides a partial characterization of (f in, =).

ν-CA are cellular automata which can have different local rules at each site of their lattice. Indeed, the spatial distribution of local rules completely characterizes ν-CA. In this paper, sets of distributions sharing some interesting properties are associated with languages of bi-infinite words. The complexity classes of these languages are...

A finite language X over an alphabet S is complete if any word in S^* is a factor of a word in X^*. A word which is not a factor of X^* is said uncompletable. Among them, some are minimal as all their proper factors belong to Fact(X^*). The problem is to find bounds on the length of the shortest minimal uncompletable words depending on k, the...

The paper investigates classes of languages of innite words with respect to the acceptance conditions of the nite automata recognizing them. Some new natural classes are compared with the Borel hierachy. In particular, it is proved that (fin, =) is as high as F R σ and G R δ. As a side eect, it is also proved that in this last case, considering...

Deterministic one-way Turing machines with sublinear space bounds are systematically studied. We distinguish among the notions of strong, weak, and restricted space bounds. The latter is motivated by the study of P automata. The space available on the work tape depends on the number of input symbols read so far, instead of the entire input. The...

Deterministic one-way Turing machines with sublinear space bounds are systematically studied. We distinguish among the notions of strong, weak, and restricted space bounds. The latter is motivated by the study of P automata. The space available on the work tape depends on the number of input symbols read so far, instead of the entire input. The...

In this paper we begin the study the dynamical behavior of non-uniform cellular automata and compare it to the behavior of " classical " cellular automata. In particular we focus on surjectivity and equicontinuity.