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Future miniaturization and mobilization of computing devices requires energyparsimonious `adiabatic' computation. This is contingent on logicalreversibility of computation. An example is the idea of quantum computationswhich are reversible except for the irreversible observation steps. We proposeto study quantitatively the exchange of computational resources like time andspace for irreversibility in computations. Reversible simulations ofirreversible computations are memory intensive. Such (polynomial time)simulations are analysed here in terms of `reversible' pebble games. We showthat Bennett's pebbling strategy uses least additional space for the greatestnumber of simulated steps. We derive a trade-off for storage space versusirreversible erasure. Next we consider reversible computation itself. Analternative proof is provided for the precise expression of the ultimateirreversibility cost of an otherwise reversible computation withoutrestrictions on time and space use. A time-irreversibility trade-off hierarchyin the exponential time region is exhibited. Finally, extremetime-irreversibility trade-offs for reversible computations in the thoroughlyunrealistic range of computable versus noncomputable time-bounds are given.Comment: 30 pages, Latex. Lemma 2.3 should be replaced by the slightly better  ``There is a winning strategy with $n+2$ pebbles and $m-1$ erasures for  pebble games $G$ with $T_G= m2^n$, for all $m \geq 1$'' with appropriate  further changes (as pointed out by Wim van Dam). This and further work on  reversible simulations as in Section 2 appears in quant-ph/970300

Reversibility and adiabatic computation: trading time and space for energy