Straight-line instruction sequence completeness for total calculation on cancellation meadows
Abstract
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 0, x 1, x -x, x x-1, x x+y, x x· 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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