Some integer formula-encodings and related algorithms
Edinah K. Gnang, Patrick Devlin

TL;DR
This paper explores special integer formulas built from addition, multiplication, and exponentiation with input 1, introducing two canonical encoding methods and algorithms for efficiently encoding large sets of integers.
Contribution
It presents two new canonical formula-encodings for integers and algorithms to efficiently determine encodings for large consecutive integer sets.
Findings
Two distinct canonical encoding methods based on decimal and arithmetic theorem
Algorithms for efficient encoding of large consecutive integers
Enhanced understanding of integer formulas and their representations
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.
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Taxonomy
TopicsCoding theory and cryptography · Numerical Methods and Algorithms · Polynomial and algebraic computation
