Multiplication, Division and Shift Instructions in Parallel Random Access Machines

Trahan, J.L., M.C. Loui and V. Ramachandran, Multiplication, division and shift instructions in parallel random access machines, Theoretical Computer Science 100 (1992) l-44. We prove that polynomial time on a parallel random access machine (PRAM) with unit-cost multiplication and division or on a PRAM with unit-cost shifts is equivalent to polynomial space on a Turing machine (PSPACE). This extends the result that polynomial time on a basic PRAM is equivalent to PSPACE to hold when the PRAM is allowed multiplication or division or unrestricted shifts. It also extends to the PRAM the results that polynomial time on a random access machine (RAM) with multiplication is equivalent to PSPACE and that polynomial time on a RAM with *A preliminary version of a portion of this work appeared in the proceedings of the 22nd Conference on Information Sciences and Systems held in 1988 at Princeton, NJ. This work was conducted at the Coordinated Science Laboratory of the University of Illinois at Urbana-Champaign with the support of the Joint Services Electronics Program (U.S. Army, U.S. Navy, U.S. Air Force) under Contract N0001484-C0149. The work of the second author was also supported in part by the National Science Foundation under grant CCR-8922008. 0304-3975/92/$05.00