In this paper we prove a lower bound of Ω(n log n) for the common element problem on two sets of size n each. Two interesting consequences of this lower bound are also discussed. In particular, we show that linear space neural network models that admit unbalanced rules cannot draw all inferences in time independent of the knowledge base size. We also show that the join operation in data base applications needs Ω(log n) time given only n processors. Comments University of Pennsylvania Department of Computer and Information Science Technical Report No. MSCIS-93-73. This technical report is available at ScholarlyCommons: http://repository.upenn.edu/cis_reports/509 A Lower Bound Result for The Common Element Problem and Its IMplication for Reflexive Reasoning MS-CIS-93-73 G R A S P LAB 356 Paul Dietz Danny Krizanc Sanguthevar Rajasekaran Loke11di-a Shastri
[1]
Lokendra Shastri,et al.
Rules and Variables in Neural Nets
,
1991,
Neural Computation.
[2]
D. R. Mani Lokendra Shastri.
A Connectionist Solution to the Multiple Instantiation Problem using Temporal Synchrony
,
1992
.
[3]
L. Shastri,et al.
From simple associations to systematic reasoning: A connectionist representation of rules, variables and dynamic bindings using temporal synchrony
,
1993,
Behavioral and Brain Sciences.
[4]
Lokendra Shastri,et al.
A Computational Model of Tractable Reasoning - Taking Inspiration from Cognition
,
1993,
IJCAI.