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Abstract
Dissipative flows model a large variety of physical systems. In this paper the evolution of such systems is interpreted as a process of computation ; the attractor of the dynamics represents the output. A framework for an algorithmic analysis of dissipative flows is presented, enabling the comparison of the performance of discrete and continuous time analog computation models. A simple algorithm for finding the maximum of n numbers is analyzed, and shown to be highly efficient. The notion of tractable (polynomial) computation in the Turing model is conjectured to correspond to computation with tractable (analytically solvable) dynamical systems having polynomial complexity.
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References
Bibliographical reference
Hava T. Siegelmann, Asa Ben-Hur and Shmuel Fishman, « Comments on Attractor Computation », CASYS, 6 | 2000, 161-170.
Electronic reference
Hava T. Siegelmann, Asa Ben-Hur and Shmuel Fishman, « Comments on Attractor Computation », CASYS [Online], 6 | 2000, Online since 19 June 2024, connection on 27 December 2024. URL : http://popups.uliege.be/3041-539x/index.php?id=182
Authors
Hava T. Siegelmann
Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel
Asa Ben-Hur
Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel
Shmuel Fishman
Department of Physics, Technion, Haifa 32000, Israel