Substitutions and Strongly Deterministic Tilesets

Abstract. Substitutions generate hierarchical colorings of the plane. Despite the non-locality of substitution rules, one can extend them by adding compatible local matching rules to obtain locally checkable colorings as the set of tilings of finite tileset. We show that the resulting tileset can furthermore be chosen strongly deterministic, a tile being uniquely determined by any two adjacent edges. A tiling by a strongly deterministic tileset can be locally reconstructed starting from any infinite path that cross every line and column of the tiling

The transitivity problem of Turing machines

International audienceA Turing machine is topologically transitive if every partial configuration — that is a state, a head position, plus a finite portion of the tape — can reach any other partial configuration, provided that it is completed into a proper configuration. We characterize topological transitivity and study its computational complexity in the dynamical system models of Turing machines with moving head, moving tape and for the trace-shift. We further study minimality, the property of every configuration reaching every partial configuration