This paper investigates one possible model of reversible computations, animportant paradigm in the context of quantum computing. Introduced byBennett, a reversible pebble game is anabstraction of reversible computation that allows to examine the space andtime complexity of various classes of problems. We present a techniquefor proving lower and upper bounds on time and space complexity for severaltypes of graphs. Using this technique we show that the time needed toachieve optimal space for chain topology is Ω(nlgn) for infinitelymany n and we discusstime-space trade-offs for chain. Further we show a tight optimalspace bound for the binary tree of height h of the form h + Θ(lg*h)and discuss space complexity for the butterfly. These results give anevidence that reversible computations need more resources than standardcomputations. We also show an upper bound on time and space complexity ofthe reversible pebble game based on the time and space complexity of thestandard pebble game, regardless of the topology of the graph.
