Pursuit and Evasion on a Ring: An Infinite Hierarchy for Parallel Real-Time Systems

Abstract.

We show that, for any positive integer n , there exists at least one timed ω -language L _n which is accepted by a 2n -processor real-time algorithm using arbitrarily slow processors, but cannot be accepted by a (2n-1) -processor real-time algorithm. It follows therefore that real-time algorithms form an infinite hierarchy with respect to the number of processors used. Furthermore, such a result holds for any model of parallel computation.