Abstract
A combination of program algebra with the theory of meadows is designed leading to a theory of computation in algebraic structures. It is proven that total functions on cancellation meadows can be computed by straight-line programs using at most five auxiliary variables. A similar result is obtained for signed meadows.
Highlights
Program algebra is an approach to the formal description of the semantics of programming languages
We prove that total functions on cancellation meadows can be represented by a normal form without tests and jumps which uses at most five auxiliary variables
Instruction sequences for functions on the rational numbers are designed in such a way that computations can be performed only with the aid of auxiliary variables to which initially the input values are copied, and from which the final values are copied to the output
Summary
Program algebra is an approach to the formal description of the semantics of programming languages. Computations over cancellation meadows can be imagined to take place on a large scale in embedded devices of various kinds Executable programs for such devices need to satisfy constraints which can hardly be formulated in the high level notation from which such programs are obtained by means of compilation. 4. We prove that total functions on cancellation meadows can be represented by a normal form without tests and jumps which uses at most five auxiliary variables. We prove that total functions on cancellation meadows can be represented by a normal form without tests and jumps which uses at most five auxiliary variables This result is extended to signed cancellation meadows—cancellation meadows that presuppose an ordering of its domain—in Sect.
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