Continued fraction algorithms, functional operators, and structure constants
Theoretical Computer Science
Analytic Analysis of Algorithms
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
A Unifying Framework for the Analysis of a Class of Euclidean Algorithms
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
An Average-Case Analysis of the Gaussian Algorithm for Lattice Reduction
Combinatorics, Probability and Computing
Sharp estimates for the main parameters of the euclid algorithm
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
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We obtain new results regarding the precise average bitcomplexity of five algorithms of a broad Euclidean type. We develop a general framework for analysis of algorithms, where the average-case complexity of an algorithm is seen to be related to the analytic behaviour in the complex plane of the set of elementary transformations determined by the algorithms. The methods rely on properties of transfer operators suitably adapted from dynamical systems theory and provide a unifying framework for the analysis of an entire class of gcd-like algorithms.