Development of physical super-turing analog hardware
In the 1930s, mathematician Alan Turing proposed a mathematical model of computation now called a Turing Machine to describe how people follow repetitive procedures given to them in order to come up with final calculation result. This extraordinary computational model has been the foundation of all modern digital computers since the World War II. Turing also speculated that this model had some limits and that more powerful computing machines should exist. In 1993, Siegelmann and colleagues introduced a Super-Turing Computational Model that may be an answer to Turing's call. Super-Turing computation models have no inherent problem to be realizable physically and biologically. This is unlike the general class of hyper-computer as introduced in 1999 to include the Super-Turing model and some others. This report is on research to design, develop and physically realize two prototypes of analog recurrent neural networks that are capable of solving problems in the Super-Turing complexity hierarchy, similar to the class BPP/log*. We present plans to test and characterize these prototypes on problems that demonstrate anticipated Super-Turing capabilities in modeling Chaotic Systems.
Physics, Astronomy, and Materials Science
Analog Computing, Hypercomputing, Neural Networks, Super-Turing Computation
Younger, A. Steven, Emmett Redd, and Hava Siegelmann. "Development of physical super-turing analog hardware." In International Conference on Unconventional Computation and Natural Computation, pp. 379-391. Springer, Cham, 2014.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)