Are parallel machines always faster than sequential machines?

Abstract

We demonstrate that parallel machines are always faster than sequential machines for a wide range of machine models, including tree Turing machine (TM), multidimensional TM, log-cost random access machine (RAM), and unit-cost RAM. More precisely, we show that every sequential machine M (in the above list) that runs in time T can be sped up by a parallel version M′ of M that runs in time o(T). All previous speedup results either rely on the severe limitation on the storage structure of M (e.g., M is a TM with linear tapes) or require that M′ has a more versatile storage structure than M (e.g., M′ is a parallel RAM (PRAM), and M is a TM with linear tapes). It is unclear whether it is the parallelism, or the restriction on the storage structures, or the combination of both that realizes such speedup. We remove all the above restrictions on storage structures in previous results. We present speedup theorems where both M and M′ use the same kind of storage medium, which is not linear tapes. Thus, we prove conclusively that parallelism alone suffices to achieve the speedup.