SIZE MATTERS: LOGARITHMIC SPACE IS REAL TIME

S.D. Bruda and S.G. Akl

Keywords

Realtime computation, timed ωlanguage, parallel complexity, reconfigurable multiple bus machine, independence system, matroid

Abstract

We show that all the problems solvable by a nondeterministic machine with logarithmic work space (NL) can be solved in real time by a parallel machine, no matter how tight the real-time constraints are. We also show that several other real-time problems are in effect solvable in nondeterministic logarithmic space once their real-time constraints are dropped and they become non-realtime. We thus conjecture that NL contains exactly all the problems that admit feasible real-time parallel algorithms. The issue of real-time optimization problems is also investigated. We identify the class of such problems that are solvable in real time. In the process, we determine the computational power of directed reconfigurable multiple bus machines (DRMBMs) with polynomially bounded resources and running in constant time, which is found to be the same as the power of directed reconfigurable networks with the same properties. We also show that write conflict resolution rules such as Priority or even Combining do not add computational power over the Collision rule, and that a bus of width 1 (a wire) suffices for any constant time computation on DRMBM.

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