TWO NON-STANDARD PARADIGMS FOR COMPUTATION: ANALOG MACHINES AND CELLULAR AUTOMATA

Serious roadblocks have been encountered in several areas of computer application, for example in the solution of intractable (NP-complete) combinatorial problems, or in the simulation of fluid flow. In this talk we will explore two alternatives to the usual kinds of computers, and ask if they provide some hope of ultimately by-passing what appear to be essential difficulties.

[1]  A. Scott,et al.  The soliton: A new concept in applied science , 1973 .

[2]  K. Steiglitz,et al.  Soliton-like behavior in automata , 1986 .

[3]  F. L. Carter The molecular device computer: Point of departure for large scale cellular automata , 1984 .

[4]  E. F. Codd,et al.  Cellular automata , 1968 .

[5]  R. Feynman Simulating physics with computers , 1999 .

[6]  R. Connelly Winning Ways for Your Mathematical Plays, Volumes I & II By Elwyn R. Berlekamp, John H. Conway , 1986 .

[7]  A. Turing On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[8]  A. Turing,et al.  On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction , 1938 .

[9]  R. Hirota,et al.  Theoretical and experimental studies of lattice solitons in nonlinear lumped networks , 1973 .

[10]  R. Sohrab Kashef,et al.  A Universal Four-State Cellular Computer , 1975, IEEE Transactions on Computers.

[11]  A. Blokhuis Winning ways for your mathematical plays , 1984 .

[12]  David S. Johnson The NP-Completeness Column: An Ongoing Guide , 1986, J. Algorithms.

[13]  Kenneth Steiglitz,et al.  Embedding Computation in One-Dimensional Automata by Phase Coding Solitons , 1988, IEEE Trans. Computers.

[14]  A. Church An Unsolvable Problem of Elementary Number Theory , 1936 .

[15]  B. Dickinson,et al.  The complexity of analog computation , 1986 .

[16]  Kenneth Steiglitz,et al.  A multi-processor cellular automaton chip , 1985, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing.

[17]  S. Wolfram Cellular automaton fluids 1: Basic theory , 1986 .

[18]  Charles H. Goldberg,et al.  Parity Filter Automata , 1988, Complex Syst..

[19]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[20]  E. Schrödinger What Is Life , 1946 .

[21]  A. Church Review: A. M. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem , 1937 .

[22]  James B. Salem,et al.  Thermodynamics and Hydrodynamics of Cellular Automata , 2010 .

[23]  David A. Plaisted,et al.  Some polynomial and integer divisibility problems are NP-HARD , 1976, 17th Annual Symposium on Foundations of Computer Science (sfcs 1976).