On Aperiodic Reversible Turing Machines (Invited Talk)

摘要

A complete reversible Turing machine bijectively transforms configurations consisting of a state and a bi-infinite tape of symbols into another configuration by updating locally the tape around the head and translating the head on the tape. We discuss a simple machine with 4 states and 3 symbols that has no periodic orbit and how that machine can be embedded into other ones to prove undecidability results on decision problems related to dynamical properties of Turing machines.