The transitivity problem of Turing machines

Anahí Gajardo (1) , Nicolas Ollinger (2) , Rodrigo Torres-Avilés (1)

1 Departamento de Ingeniería Matemática
2 LIFO - Laboratoire d'Informatique Fondamentale d'Orléans

A 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.

Mots clés: reversible computing; computability; topological dynamics; symbolic dynamics; discrete dynamical systems

Domaines: Autre [cs.OH]

Anahí Gajardo, Nicolas Ollinger, Rodrigo Torres-Avilés. The transitivity problem of Turing machines. Mathematical Foundations of Computer Science 2015 - 40th International Symposium (MFCS 2015), Aug 2015, Milan, Italy. pp. 231-242, ⟨10.1007/978-3-662-48057-1_18⟩. ⟨hal-01145799⟩