Straight-line instruction sequence completeness for total calculation on cancellation meadows

Details Straight-line instruction sequence completeness for total calculation on cancellation meadows Straight-line instruction sequence completeness for total calculation on cancellation meadows

2009-05-28

arxiv.org/abs/0905.4612v2

Computer Science

Logic in Computer Science

24 pages

Scientific paper

A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures which use in addition to a zero test and copying instructions the instruction set $\{x \Leftarrow 0, x \Leftarrow 1, x\Leftarrow -x, x\Leftarrow x^{-1}, x\Leftarrow x+y, x\Leftarrow x\cdot y\}$. It is proven that total functions on cancellation meadows can be computed by straight-line programs using at most 5 auxiliary variables. A similar result is obtained for signed meadows.

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