A program-size complexity measure for mathematical problems and conjectures

Abstract

Cristian Calude et al. in [5] have recently introduced the idea of measuring the degree of difficulty of a mathematical problem (even those still given as conjectures) by the length of a program to verify or refute the statement. The method to evaluate and compare problems, in some objective way, will be discussed in this note. For the practitioner, wishing to apply this method using a standard universal register machine language, we provide (for the first time) some "small" core subroutines or library for dealing with array data structures. These can be used to ease the development of full programs to check mathematical problems that require more than a predetermined finite number of variables. © 2012 Springer-Verlag.