A reversible Turing machine is one whose transition function is 1, so that no instantaneous description (ID) has more than one predecessor. Using a pebbling argument, this paper shows that, for any e > 0, ordinary multitape Turing machines using time T and space S can be simulated by reversible ones using time O(T +) and space O(S log T) or in linear time and space O(ST). The former result implies in particular that reversible machines can simulate ordinary ones in quadratic space. These

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... refer to reversible machines that save their input, thereby insuring a global 1:1 relation between initial and final Ds, even when the function being computed is many-to-one. Reversible machines that instead erase their input can of course compute only 1:1 partial recursive functions and indeed provide a G6del numbering of such functions. The time/space cost of computing a 1:1 function on such a machine is equal within a small polynomial to the cost of computing the function and its inverse on an ordinary Turing machine.