Internationally recognised researchers look at developing trends in combinatorics with
applications in the study of words and in symbolic dynamics. They explain the important …

We study a general class of Euclidean algorithms which compute the greatest common
divisor [gcd], and we perform probabilistic analyses of their main parameters. We view an …

We provide sharp estimates for the probabilistic behaviour of the main parameters of the
Euclid Algorithms, both on polynomials and on integer numbers. We study in particular the …

We provide sharp estimates for the probabilistic behaviour of the main parameters of the
Euclid algorithm, and we study in particular the distribution of the bit-complexity which …

There exist fast variants of the gcd algorithm which are all based on principles due to Knuth
and Schönhage. On inputs of size n, these algorithms use a Divide and Conquer approach …

The binary Euclidean algorithm is a modification of the classical Euclidean algorithm for
computation of greatest common divisors which avoids ordinary integer division in favour of …

There exist fast variants of the gcd algorithm which are all based on principles due to Knuth
and Schönhage. On inputs of size n, these algorithms use a Divide and Conquer approach …

The present study describes the main algorithms devoted to solving the lattice reduction
problem. This is a central algorithmic problem, due to its intrinsic theoretical interest …

Gcd computation is a widely used routine in computations on long integers. It is omnipresent
in rational computations, public key cryptography or computer algebra. Many gcd algorithms …

A measure of randomness on the unit interval I:=[0, 1] tests how a sequence XI differs from a
“truly random” sequence. See books (Drmota and Tichy, 1997; Kuipers and Niederreiter …