4 research outputs found
Straight-line instruction sequence completeness for total calculation on cancellation meadows
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 . 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.Comment: 24 page
Division by zero in non-involutive meadows
Meadows have been proposed as alternatives for fields with a purely
equational axiomatization. At the basis of meadows lies the decision to make
the multiplicative inverse operation total by imposing that the multiplicative
inverse of zero is zero. Thus, the multiplicative inverse operation of a meadow
is an involution. In this paper, we study `non-involutive meadows', i.e.\
variants of meadows in which the multiplicative inverse of zero is not zero,
and pay special attention to non-involutive meadows in which the multiplicative
inverse of zero is one.Comment: 14 page