Rounds versus Time for the Two Person Pebble Game (Extended Abstract)

We show the following results for rounds/time tradeoffs in the two person pebble game. 1. For every R and n (R =O (n /logn )), there is a bounded degree graph of n vertices for which the Pebbler can win in R rounds only in time Ω(n /logR ). 2. There is a graph that exhibits almost tight round/time tradeoffs for all rounds. 3. There is no graph with tight round/time tradeoffs for all rounds. As a consequence, we improve the simulation of bounded fan-in circuits by unbounded fan-in circuits, extending the size/depth tradeoff of Paterson and Valiant. Below is the list of symbols used in the paper, other than Latin characters and Arabic numerals. Lower case roman l is not used. Similarly, upper case roman O is not used (while italic O is). lower case Greek letters α, ε, θ upper case Greek letter Ω mathematical symbols ( ) { } < > ≤ ≥ = + ⊆ | ∈ summation symbol Σ end of proof `