On topological dynamics of Turing machines

AbstractWe associate to a Turing machine two dynamical systems which we call Turing machine with moving tape (TMT) and Turing machine with moving head (TMH). TMT are equivalent to generalized shifts of Moore (1990) and they include two-sided full shifts. TMH are shift-commuting maps of two-sided sofic systems. In both classes we characterize systems with the shadowing property, show that a bijective expansive TMT is conjugate to a subshift of finite type and that topological entropy of every TMH is zero. We conjecture that every TMT has a periodic point