On entropy and Turing machine with moving tape dynamical model

If M is a Turing machine with the states set Q and the alphabet , then it induces the continuous map T on the compact metric space (the Turing machine with moving tape (TMT) model).

This paper mainly deals with the topological entropy of the map T. We give the simple formula for topological entropy of the TMT model. The exact conditions for T being homeomorphism are also presented.

Additionally we study connections between the dynamics of T and the induced shift dynamics. Obtained results are used to calculate the exact value of topological entropy among some class of invertible TMT. The entropy upper bound is also given in other, more general, situations.