Sofic one head machines

Anahi Gajardo (1)

1 Departamento de Ingeniería Matemática

There are several systems consisting in an object that moves on the plane by following a given rule. It is frequently observed that these systems eventually fall into an unexplained repetitive movement. The general framework of k-dimensional Turing machines with only one head is adopted. A subshift is associated to each Turing machine, and its properties are studied. The subshift consists in the set of sequences of symbols that the machine reads together with the states that it has through each evolution. The focus is placed on the machines whose associated subshift is sofic. These machines cannot make long tours, i.e., the time between two consecutive visits to a given cell is bounded, and this property characterises them. It is proved that all of these machines eventually fall into a repetitive movement when starting over an initially periodic coloration. Nevertheless, it seems that the machines with a sofic subshift are too simple. Many known machines remain out of scope. As an example, the 0,1 and 2 pebble automata with 1 symbol are studied.

Domaines: Autre [cs.OH]

Anahi Gajardo. Sofic one head machines. JAC 2008, Apr 2008, Uzès, France. pp.54-64. ⟨hal-00273938⟩