Nondeterministic Turing Machine Computer Architecture for Efficient Processing Using Spatial Relationships

Abstract

A nondeterministic Turing machine (NTM) performs computations, such as factorization and arithmetic, using a spatial binary enumeration system, a three-dimensional relation system, a simulated-human logic system, and a bijective-set memory system. The NTM may be constructed by a deterministic Turing machine (DTM) using the four systems listed above.

1 . A computer implemented nondeterministic Turing machine, the nondeterministic Turing machine comprising:
 a knowledgebase containing data representing a plurality of objects, data representing a plurality of classes, and data representing relationships between the plurality of objects and the plurality of classes;   an induction module comprising means for generating data representing a concept represented by a plurality of inputs representing the plurality of objects and for storing the data representing the concept in the knowledgebase;   a deduction module for retrieving, from the knowledgebase, data representing a class containing an object represented by an input to the deduction module;   a reduction module for retrieving, from the knowledgebase, data representing an object which is a member of a class represented by an input to the reduction module;   a cognitive logic unit adapted to:   (1) store data representing a product P in the knowledgebase as a spatial binary number having a first plurality of spatial binary bits;   (2) create and store a mapping of the first plurality of spatial binary bits to x, y, and z dimensions in a first repeating pattern in the knowledgebase;   (3) obtain a complement C of the product P, wherein the complement C includes a second plurality of spatial binary bits;   wherein C=1n2−P;   wherein B is equal to the number of bits in P;   wherein n=(B/2) if B is even;   wherein n=(B+1)/2 if B is odd;   wherein 1n2 is a binary number of length n consisting solely of 1s;   (4) create and store a mapping of the second plurality of spatial binary bits to the x, y, and z dimensions in a second repeating pattern;   (5) construct an empty diagonal form representation of partial products of a first and second factor of the product P;   (6) recursively fill the diagonal form representation with a third plurality of spatial binary bits based on the product P and a divider D; and   (7) identify the first and second factor of the product P based on the filled diagonal form representation;   wherein the data representing the plurality of objects represent the plurality of objects in the form of three-dimensional representations of a fourth plurality of spatial binary bits; and   wherein the data representing the plurality of classes represent the plurality of classes in the form of three-dimensional representations of a fifth plurality of spatial binary bits;   wherein the plurality of inputs and a current state of the nondeterministic Turing machine does not determine at least one of: (1) the data representing the class, and (2) the data representing the object;   wherein each of the first, second, third, fourth, and fifth pluralities of spatial binary bits has a value selected from the set consisting of −1 and +1.