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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
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                        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.