Li, Ming; Vitányi, Paul Reversibility and adiabatic computation: Trading time and space for energy. (English) Zbl 0869.68019 Proc. R. Soc. Lond., Ser. A 452, No. 1947, 769-789 (1996). Summary: Future miniaturization and mobilization of computing devices requires energy parsimonious ‘adiabatic’ computation. This is contingent on logical reversibility of computation. An example is the idea of quantum computations which are reversible except for the irreversible observation steps. We propose to study quantitatively the exchange of computational resources like time and space for irreversibility in computations. Reversible simulations of irreversible computations are memory intensive. Such (polynomial time) simulations are analyzed here in terms of ‘reversible’ pebble games. We show that Bennett’s pebbling strategy uses least additional space for the greatest number of simulated steps. We derive a trade-off for storage space versus irreversible erasure. Next, we consider reversible computation itself. An alternative proof is provided for the precise expression of the ultimate irreversibility cost of an otherwise reversible computation without restrictions on time and space use. A time-irreversibility trade-off hierarchy in the exponential time region is exhibited. Finally, extreme time-irreversibility trade-offs for reversible computations in the thoroughly unrealistic range of computable versus non-computable time-bounds are given. Cited in 1 ReviewCited in 11 Documents MSC: 68M99 Computer system organization 68M01 General theory of computer systems Keywords:logical reversibility of computation PDFBibTeX XMLCite \textit{M. Li} and \textit{P. Vitányi}, Proc. R. Soc. Lond., Ser. A 452, No. 1947, 769--789 (1996; Zbl 0869.68019) Full Text: DOI arXiv