Some integer formula-encodings and related algorithms
Combinatorics
2013-03-05 v1 Logic in Computer Science
Abstract
We investigate the special class of formulas made up of arbitrary but finite com- binations of addition, multiplication, and exponentiation gates. The inputs to these formulas are restricted to the integral unit 1. In connection with such formulas, we describe two essen- tially distinct families of canonical formula-encodings for integers, respectively deduced from the decimal encoding and the fundamental theorem of arithmetic. Our main contribution is the de- tailed description of two algorithms which efficiently determine the canonical formula-encodings associated with relatively large sets of consecutive integers.
Cite
@article{arxiv.1303.0325,
title = {Some integer formula-encodings and related algorithms},
author = {Edinah K. Gnang and Patrick Devlin},
journal= {arXiv preprint arXiv:1303.0325},
year = {2013}
}