The power of parallel time

In this thesis, we address the following question: Are parallel machines always faster than sequential machines? Our approach is to examine the common machine models of sequential computation. For each such machine ${\cal M}$ that runs in time T, we determine whether it is possible to speed up ${\cal M}$ by a "parallel version" ${\cal M}\sp\prime$ of ${\cal M}$ that runs in time o(T). We find that the answer is affirmative for a wide range of machine models, including the tree Turing machine, the multidimensional Turing machine, the log-cost RAM (random access machine), the unit-cost RAM, and the pointer machine. All previous speedup results either relied on the severe limitation on the storage structure of ${\cal M}$ (e.g., ${\cal M}\sp\prime$ was a Turing machine with linear tapes) or required that ${\cal M}\sp\prime$ had a more versatile storage structure than ${\cal M}$ (e.g., ${\cal M}\sp\prime$ was a PRAM (parallel RAM), and ${\cal M}$ was a Turing machine with linear tapes). It was unclear whether it was the parallelism or the restriction on the storage structures (or the combination of both) that realized such speedup. We remove the above restrictions on storage structures in previous results. We present speedup theorems where the storage medium of ${\cal M}\sp\prime$ is the same as (or even weaker than) that of ${\cal M}$. Hence, parallelism alone suffices to achieve a speedup. One implication is that there does not exist any recursive function that is "inherently not parallelizable."U of I OnlyETDs are only available to UIUC Users without author permissio