The Greatest Integer Function

A Greatest Integer Theorem for Fibonacci Spaces

defined by u% + MUQ+J = u^+2The latter is shown to be true in all cases but one, and in slightly revised form in the remaining case. Z A GENERAL ASYMPTOTIC THEOREM With the polynomial fix) = -ag-a-jX an.fx " +x = (x rj) -(x rn), a,integers, r-j real, /y distinct, |/y| < 1 for / > 2, we associate the /7-space C(f) of all (complex) sequences S =is0,sif—J in which SQ, —, sn-i are arbitrary, but ha...

Computing the integer partition function

In this paper we discuss efficient algorithms for computing the values of the partition function and implement these algorithms in order to conduct a numerical study of some conjectures related to the partition function. We present the distribution of p(N) for N ≤ 109 for primes up to 103 and small powers of 2 and 3.

On primitive recursive algorithms and the greatest common divisor function

We establish linear lower bounds for the complexity of non-trivial, primitive recursive algorithms from piecewise linear given functions. The main corollary is that logtime algorithms for the greatest common divisor from such givens (such as Stein’s) cannot be matched in efficiency by primitive recursive algorithms from the same given functions. The question is left open for the Euclidean algor...

Utilitarianism: The Greatest Good for the Greatest Number

Least and greatest fixed points of a while semantics function

The meaning of a program is given by specifying the function (from input to output) that corresponds to the program. The denotational semantic definition, thus maps syntactical things into functions. A relational semantics is a mapping of programs to relations. We consider that the input-output semantics of a program is given by a relation on its set of states. In a nondeterministic context, th...