Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/18/84; site utcsrgv.UUCP Path: utzoo!utcsrgv!eas From: eas@utcsrgv.UUCP (Ann Struthers) Newsgroups: ont.events Subject: Theoretical Aspects Seminar Message-ID: <666@utcsrgv.UUCP> Date: Wed, 16-Jan-85 13:41:22 EST Article-I.D.: utcsrgv.666 Posted: Wed Jan 16 13:41:22 1985 Date-Received: Wed, 16-Jan-85 14:50:32 EST Distribution: ont Organization: CSRI, University of Toronto Lines: 39 THEORETICAL ASPECTS SEMINAR Thursday, January 24, 1985 4:00 P.M. SF 1105 Mr. Robert Wilber Carnegie-Mellon University Pittsburgh "White Pebbles Help" Abstract: The black pebble game is a one player game played on a directed acyclic graph. Black pebbles are placed on and removed from vertices of the dag according to rules that model the deterministic evaluation of a straight- line program. The number of pebbles needed to pebble a dag is equal to the number of registers needed to evaluate the corresponding straight- line program. The black-white pebble game is an extension of the black pebble game in which white pebbles are used to model nondeterministic guesses that can be made at any time but must eventually be verified. The number of pebbles needed to pebble a dag in the black-white pebble game is equal to the number of registers needed to evaluate the corres- ponding straight-line program by a nondeterministic strategy. I construct a family of dags with vertex in degrees bounded by 2 such 2 that the nth dag can be pebbled with 0(n ) pebbles in the black-white pebble game but for which any strategy of the black pebble game requires 2 w(n ) pebbles. This shows that there are straight-line programs that can be evaluated nondeterministically with asymptotically less space than is required by any deterministic evaluation.