# Efficient simulations of simple models of parallel computation by time-bounded ATM's and space-bounded TM's

## Abstract

We present efficient time-bounded ATM and space-bounded TM simulations of one-way conglomerates (OWC's), which are interconnected networks of finite-state machines that allow only one-way communication between adjacent nodes. In particular, we show that OWC's with depth *D*(*n*) and operating in time *T*(*n*) can be simulated by ATM's in time *O*(*D*(*n*) · log *T*(*n*)) (and hence by a TM with the same amount of space). This extends Ruzzo's result that boolean circuits of depth *D*(*n*) can be simulated by *O*(*D*(*n*))-time bounded ATM's, and refines Goldschlager's result that two-way conglomerates operating in *T*(*n*) time can be simulated by *T*(*n*)-space bounded TM's. By exploiting the regularity of interconnections in some OWC's, we obtain more efficient space-bounded TM simulations. For example, using the ATM result, a *k*-dimensional one-way mesh array of *n*^{ k }-nodes would require *n*^{2} space on a TM (such an array can run in *c*^{ n } time in the worst case). We show that the space can be reduced to *n*^{2−1/k}.

## Keywords

Input Node Combinational Circuit Boolean Circuit Input Tape Full Binary Tree## Preview

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