Data Independence of Read, Write, and Control Structures in PRAM Computations

under the title \Data-independences of parallel random access machines." Abstract We introduce the notions of control and communication structures in PRAM computations and relate them to the concept of data-independence. Our main result is to characterize diierences between unbounded fan-in parallelism AC k , bounded fan-in par-allelism NC k , and the sequential classes DSPACE(log n) and LOGDCFL in terms of a PRAM's communication structure and instruction set. Our ndings give a concrete indication that in parallel computations writing is more powerful than reading. Further characterizations are given for parallel pointer machines and the semi-unbounded fan-in circuit classes SAC k. In particular, we obtain the rst characterizations of NC k and DSPACE(log n) in terms of PRAM's. Finally, we introduce Index-PRAM's which in some sense have \built-in data-independence." We propose Index-PRAM's as a tool for the development of data-independent parallel algorithms. Index-PRAM's serve for studying the essential diierences between the above mentioned complexity classes with respect to the underlying instruction set used.