International audienceThe 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 specially suited for non-uniform cellular automata

International audienceIn 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

International audienceThis 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 languages of bi-innite words. The complexity classes of these languages are investigated providing an initial rough classica-tion of ν-CA

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 class of functions space constructible by such machines is investigated, and it is shown that every function f that is space constructible by a deterministic two-way Turing machine, is space constructible by a strongly f space-bounded deterministic one-way Turing machine as well. We prove that the restricted mode coincides with the strong mode for space constructible functions. The known infinite, dense, and strict hierarchy of strong space complexity classes is derived also for the weak mode by Kolmogorov complexity arguments. Finally, closure properties under AFL operations, Boolean operations and reversal are shown.

Abstract. The aim in solving puzzles is to find the solution using several clues and restrictions. In this paper, we solve a numerical puzzle, the n-fractions puzzle, by constraint programming. The n-fractions puzzle is problem 41 of the CSPLib, a library of test problems for constraint solvers. Models referenced in the CSPLib return invalid solutions as soon as the number n of fractions exceeds five. To solve the n-fractions puzzle, we first provide an upper bound for the unsatisfiability inspired by constraint filtering techniques. Then we propose two new constraint programming models that exploit the integer factorization of the fractions' denominators and their lowest common multiple. The proposed models can solve up to the 19-fractions puzzle within a few minutes and without returning invalid solutions. Some restrictions of the models that eliminate invalid solutions still allow them to solve larger n-fractions puzzles, even if the solving times increase. At the end, only six n-fractions puzzles remain open.