Simulating Shared Memory in Real Time: On the Computation Power of Reconfigurable Architectures

Abstract

We consider randomized simulations of shared memory on a distributed memory machine (DMM) where the n processors and the n memory modules of the DMM are connected via a reconfigurable architecture. We first present a randomized simulation of a CRCW PRAM on a reconfigurable DMM having a complete reconfigurable interconnection. It guarantees delay O (log * n ), with high probability. Next we study a reconfigurable mesh DMM (RM-DMM). Here the n processors and n modules are connected via an n × n reconfigurable mesh. It was already known that an n × m reconfigurable mesh can simulate in constant time an n -processor CRCW PRAM with shared memory of size m . In this paper we present a randomized step by step simulation of a CRCW PRAM with arbitrarily large shared memory on an RM-DMM. It guarantees constant delay with high probability, i.e., it simulates in real time. Finally we prove a lower bound showing that size Ω ( n 2 ) for the reconfigurable mesh is necessary for real time simulations.