Reversal Complexity: (Extended Abstract)

The importance of reversal complexity as a basic computational resource has only been recognized in recent years. It is intimately connected to parallel time complexity and circuit depth. In this paper, we develop some basic techniques necessary for establishing analogues of well-known theorems on space and time complexity. Our main results are that for reversal-constructible functions s(n) ≥ logn DSPACE(s(n)) ⊆ DREVERSAL(s(n)) and the first tape-reduction theorem. As applications of the tape reduction theorem, we prove a hierarchy theorem and show the existence of complete languages for reversal complexity.