Related papers: On Cornacchia's Algorithm

We present a new variant of the Faa di Bruno formula with a simpler summation order.

Knuth [12, Page 417] states that "the (program of the) Fibonaccian search technique looks very mysterious at first glance" and that "it seems to work by magic". In this work, we show that there is even more magic in Fibonaccian (or else…

A new class of functions is presented. The structure of the algorithm, particularly the selection criteria (branching), is used to define the fundamental property of the new class. The most interesting property of the new functions is that…

In this paper we establish that the well-known Arithmetic System is consistent in the traditional sense. The proof is done within this Arithmetic System.

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

This letter introduces a new, substantially simplified version of the branching recurrence operation of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html), and proves its equivalence to the old, "canonical" version.

Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…

Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…

The paper briefly introduces multiple classifier systems and describes a new algorithm, which improves classification accuracy by means of recommendation of a proper algorithm to an object classification. This recommendation is done…

Ackermann's function can be expressed using an iterative algorithm, which essentially takes the form of a term rewriting system. Although the termination of this algorithm is far from obvious, its equivalence to the traditional recursive…

Two very fast and simple O(lg n) algorithms for individual Fibonacci numbers are given and compared to competing algorithms. A simple O(lg n) recursion is derived that can also be applied to Lucas. A formula is given to estimate the largest…

In this paper we prove the correctness of Dijkstra's algorithm. We also discuss it and at the end we show an application.

We present arguments for the formulation of unified approach to different standard continuous inference methods from partial information. It is claimed that an explicit partition of information into a priori (prior knowledge) and a…

We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…

A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.

These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…

Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical…

In this paper we relate a number of parsing algorithms which have been developed in very different areas of parsing theory, and which include deterministic algorithms, tabular algorithms, and a parallel algorithm. We show that these…

This is a comment on a recent publication claiming to have found a ``quantum optimization'' algorithm which outperforms known algorithms for minimizing some ``cost function''. Unfortunately, this algorithm is no better than choosing a state…

The starting point of this paper is a collection of properties of an algorithm that have been distilled from the informal descriptions of what an algorithm is that are given in standard works from the mathematical and computer science…