Impossibility Results for Asynchronous PRAM

In the asynchronous PRAM model processes communicate by atomically read ing and writing shared memory locations This paper investigates the extent to which asynchronous PRAM permits long lived highly concurrent data struc tures An implementation of a concurrent object is non blocking if some op eration will always complete in a nite number of steps it is wait free if every operation will complete in a nite number of steps and it is k bounded wait free for some k if every operation will complete within k steps It is known that asynchronous PRAM cannot be used to construct a non blocking implemen tation of any object that solves two process consensus a class of objects that includes many common data types It is natural to ask whether the converse holds does asynchronous PRAM permit non blocking implementations of any object that does not solve consensus This papers shows that the answer is no There is a strict in nite hierarchy among objects that do not solve consensus there exist objects without non blocking implementations with imple mentations that are non blocking but not wait free with implementations that are wait free but not bounded wait free and with implementations that are K bounded wait free but not k bounded wait free for all k and some K k This paper will appear in the Third Annual ACM Symposium on Parallel Algo rithms and Architectures July Hilton Head South Carolina c Digital Equipment Corporation All rights reserved