Space-Efficient Reversible Simulations

We study constructions that convert arbitrary deterministic Turing machines to reversible machines; i.e. reversible simulations. Specifically, we study space-efficient simulations; that is, the resulting reversible machine uses O(f(S)) space, where S is the space usage of the original machine and f is very close to linear (say, n log n or smaller). We generalize the previous results on this reversibility problem by proving a general theorem incorporating two simulations: one is space-efficient (O(S)) and is due to Lange, McKenzie, and Tapp[5]; the other is time-efficient (O(T ) for any 2 > 0, where T is the time usage of the original machine) and is due to Bennett[2]. Corollaries of our general theorem give interesting new time-space tradeoffs. One is that for any unbounded space constructible f(n) = o(T (n)), there is a reversible simulation using O(S log f(S)) space and O(f(S)c) time, for any 2 > 0. This gives the first reversible simulation that uses time subexponential in T , and space subquadratic in S.