A nondeterministic Turning 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 implementing a 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 numbers 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 numbers 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 the 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. 2. The computer of claim 1, wherein the cognitive logic unit comprises means for receiving an input and for triggering the induction module to perform induction on the input and on data stored in the knowledgebase to generate a representation of a class containing an object represented by the input. 3. The computer of claim 1, wherein the cognitive logic unit comprises means for receiving an input and for triggering the deduction module to perform deduction on the input and on data stored in the knowledgebase to retrieve, from the knowledgebase, data representing a class containing an object represented by the input. 4. The computer of claim 1, wherein the cognitive logic unit comprises means for receiving an input and for triggering the reduction module to perform deduction on the input and on data stored in the knowledgebase to retrieve, from the knowledgebase, data representing an object which is a member of a class represented by the input. 5. The computer of claim 1, wherein the deduction module comprises means for retrieving the data representing the class by performing a set operation on data in the knowledgebase. 6. The computer of claim 1, wherein the reduction module comprises means for retrieving the data representing the object by performing a set operation on data in the knowledgebase. 7. The computer of claim 1, wherein (7) comprises identifying the first factor based on a first edge of the diagonal form representation. 8. The computer of claim 7, wherein (7) comprises identifying the second factor based on a second edge of the diagonal form representation. 9. The computer of claim 1, wherein recursively filling the diagonal form representation in (6) includes a first step comprising copying the value of the leftmost bit of the product P into the four corners of the diagonal form representation. 10. The computer of claim 9, wherein (6) includes a second step comprising subtracting the values in the four corners of the diagonal form representation from corresponding bits of the product to produce a modified product. 11. The computer of claim 9, wherein (6) includes a third step comprising copying the inverse of the leftmost bit of the complement C into bits in the diagonal form representation which are adjacent to the four corners of the diagonal form representation. 12. The computer of claim 11, wherein (6) includes a fourth step comprising applying a parallel rule to the diagonal form representation, wherein the parallel rule specifies that: any row in the diagonal form representation that contains a zero must contain all zeroes; and any diagonal column in the diagonal form representation that begins with a zero must contain all zeroes. 13. A method for use with a computer implementing a nondeterministic Turing machine, the nondeterministic Turing machine including a knowledgebase, wherein the knowledgebase contains 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, wherein the method comprises: (1) 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; (2) retrieving, from the knowledgebase, data representing a class containing an object represented by an input to the deduction module; (3) retrieving, from the knowledgebase, data representing an object which is a member of a class represented by an input to the reduction module; (4) storing data representing a product P in the knowledgebase as a spatial binary number having a first plurality of spatial binary bits; (5) creating and storing a mapping of the first plurality of spatial binary bits to x, y, and z dimensions in a first repeating pattern in the knowledgebase; (6) obtaining 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; (7) creating and storing a mapping of the second plurality of spatial binary bits to the x, y, and z dimensions in a second repeating pattern; (8) constructing an empty diagonal form representation of partial products of a first and second factor of the product P; (9) recursively filling the diagonal form representation with a third plurality of spatial binary bits based on the product P and the divider D; and (10) identifying 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 first 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 second 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 and second pluralities of spatial binary bits has a value selected from the set consisting of −1 and +1. 14. The method of claim 13, wherein (7) comprises identifying the first factor based on a first edge of the diagonal form representation. 15. The method of claim 14, wherein (7) comprises identifying the second factor based on a second edge of the diagonal form representation. 16. The method of claim 13, wherein recursively filling the diagonal form representation in (6) includes a first step comprising copying the value of the leftmost bit of the product P into the four corners of the diagonal form representation. 17. The method of claim 16, wherein (6) includes a second step comprising subtracting the values in the four corners of the diagonal form representation from corresponding bits of the product to produce a modified product. 18. The method of claim 17, wherein (6) includes a third step comprising copying the inverse of the leftmost bit of the complement C into bits in the diagonal form representation which are adjacent to the four corners of the diagonal form representation. 19. The method of claim 18, wherein (6) includes a fourth step comprising applying a parallel rule to the diagonal form representation, wherein the parallel rule specifies that: any row in the diagonal form representation that contains a zero must contain all zeroes; and any diagonal column in the diagonal form representation that begins with a zero must contain all zeroes.