Title :
Computation by dynamical systems
Author :
Siegelmann, H.T. ; Fishman, Shmuel
Author_Institution :
Fac. of Ind. Eng. & Manage., Technion-Israel Inst. of Technol., Haifa, Israel
Abstract :
A theory for computation by dynamical systems is presented, definition of computation time that is applicable for systems that are continuous as well as for systems that are discrete in time, based on a physical time scale is introduced. Computational complexity of dynamical systems is explored. For this purpose the standard classes of computer science are adapted to dynamical systems. The complexity classes Pd , BPPd and NPd corresponding to the standard classes P, BPP and NP are defined for the case of more physical dynamics. It is then shown that computation of a simple fixed point is in Pd or BPPd (depending on the output decision process) while for an isolated strange attractor it is in NPd. The computation by the continuous Hopfield neural network is analyzed in detail and found to be in Pd or in BPP d
Keywords :
Hopfield neural nets; computation theory; computational complexity; discrete time systems; BPPd complexity class; NPd complexity class; Pd complexity class; computation theory; computation time; computational complexity; continuous Hopfield neural network; dynamical systems; isolated strange attractor; output decision process; physical time scale; Analog computers; Chaos; Milling machines; Neural networks; Neurodynamics; Orbits; Physics computing; State-space methods; Testing; Turing machines;
Conference_Titel :
Systems, Man, and Cybernetics, 1997. Computational Cybernetics and Simulation., 1997 IEEE International Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-4053-1
DOI :
10.1109/ICSMC.1997.638181
