Long multiplication by instruction sequences with backward jump instructions
Abstract
For each function on bit strings, its restriction to bit strings of any given length can be computed by a finite instruction sequence that contains only instructions to set and get the content of Boolean registers, forward jump instructions, and a termination instruction. Backward jump instructions are not necessary for this, but instruction sequences can be significantly shorter with them. We take the function on bit strings that models the multiplication of natural numbers on their representation in the binary number system to demonstrate this by means of a concrete example. The example is reason to discuss points concerning the halting problem and the concept of an algorithm.
Cite
@article{arxiv.1312.1812,
title = {Long multiplication by instruction sequences with backward jump instructions},
author = {J. A. Bergstra and C. A. Middelburg},
journal= {arXiv preprint arXiv:1312.1812},
year = {2014}
}
Comments
17 pages, the preliminaries are about the same as the preliminaries in arXiv:1308.0219 [cs.PL] and arXiv:1312.1529 [cs.PL]; minor errors corrected, references added; section on indirect addressing added