Titlebook: Combinatorics, Computability and Logic; Proceedings of the T C. S. Calude,M. J. Dinneen,S. Sburlan Conference proceedings 2001 Springer-Ver

Projection

Some Results for Some Conjectures in Addition Chains0 ≤ ., . < .. The smallest length . for which an addition chain for . exists is denoted by .(.). Scholz conjectured that .(2. − 1) ≤ . + .(.) − 1. Aiello and Subbarao proposed a stronger conjecture which is “. ≥ 1, . 2. − 1 . − 1.” This paper improves Brauer’s result for the Scholz conjecture. We pr

MUTED

A Highly Random Number define . as the probability that an arbitrary machine be circular and we prove that . is a random number that goes beyond ., the probability that a universal self delimiting machine halts. The algorithmic complexity of . is strictly greater than that of ., but similar to the algorithmic complexity

vector

Dini’s Theorem: A Constructive Case Studysince it fails in the recursive model. Nevertheless, a basic constructive version of the theorem is proved, as is a version in which the uniform convergence of the sequence of functions is reduced to the convergence of some subsequence of a particular sequence of real numbers. After some additional