# An automatic speed-up of random access machines with powerful arithmetic instructions

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## Abstract

*Speeding up automatically* means to find a parallel algorithm for an arbitrary sequential one, so that the time for designing this parallel algorithm plus its runtime is considerably lower than the time sequentially used. Here we consider sequential and parallel random access machines (RAMs, PRAMs) with arithmetic instructions {+, −, *}. RAMs work on integer inputs and use direct and a restricted form of indirect addressing, only.

We extend the result of *Meyer auf der Heide* ([MEYE86]) to RAMs which can also multiply. We use techniques for fast parallel computation of polynomials due to *Valiant, Skyum, Berkowitz* and *Rackoff* ([VSBR83]). In order to apply this we have to make their simulation *uniform*. This result, interesting in itself, is based on an efficient parallelization of *straight-line programs* with operations {+,*max*}.

With a PRAM with a processors we gain a speed up factor of \(\frac{{(log log q)^2 + log log q \cdot log D}}{{log q}}\)for any *uniform* RAM P, where D denotes the *formal degree* of the polynomials computed by P.

## Keywords

Parallel Algorithm Arithmetic Circuit Formal Degree Common Memory Random Access Machine## Preview

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## References

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