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.
Please help me write a proper abstract based on the patent claims. CLAIM: 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.