2013/03/02 by Edinah K. Gnang, Gnang, Edinah K., Patrick Devlin +1
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Logic in Computer Science (cs.LO) #cs.LO #math.CO
paper · pdf · doi:10.48550/arxiv.1303.0325
arxiv created 2013/03/02 · arxiv updated 2013/03/05
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.