Efficient Simulations of Simple Models of Parallel Computation by Time-Bounded ATM's and Space-Bounded TM's

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 n2 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 n2−1/k.