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 $\{x\Leftarrow 0,x\Leftarrow 1,x\Leftarrow -x,x\Leftarrow x^{-1},x\Leftarrow x+y,x\Leftarrow x\cdot y\}$. 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.

24 pages

References in corpus (1)

• The initial meadows