Time and Space Complexity of Reversible Pebbling

摘要

In the context of quantum computing, reversible computations play an important role. In this paper the model of the reversible pebble game introduced by Bennett is considered. Reversible pebble game is an abstraction of a reversible computation, that allows to examine the space and time complexity for various classes of problems. We present techniques for proving lower and upper bounds on time and space complexity. Using these techniques we show a partial lower bound on time for optimal space (time for optimal space is not o(n lg n)) and a time-space tradeoff (space O( n~(1/k)) for time 2~kn) for a chain of length n. Further, we show a tight optimal space bound (h + Θ(lg~* h)) for a binary tree of height h and we discuss space complexity for a butterfly. By these results we give an evidence, that for reversible computations more resources are needed with respect to standard irreversible computations.