Reversibility and Adiabatic Computation: Trading Time and Space for Energy

TL;DR

This paper investigates the trade-offs between time, space, and energy in reversible and adiabatic computation, providing theoretical bounds and strategies for optimizing resource use in energy-efficient computing.

Contribution

It introduces a formal analysis of resource trade-offs in reversible computation using pebble games and derives bounds on irreversibility costs and time-irreversibility hierarchies.

Findings

Bennett's pebbling strategy minimizes space for simulating irreversible computations.

A trade-off between storage space and irreversible erasure is established.

Reversible computation irreversibility costs are precisely characterized.

Abstract

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 analysed 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 noncomputable time-bounds are given.