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.

Abstract: A computer system aligns two or more sequences with each other to identify similarities and differences between the aligned sequences. The sequences may, for example, represent proteins. The system performs alignment quickly and accurately by representing the sequences as perceptual information and conceptual information having mappings between them in a knowledgebase, and then performing the alignment based on the representations of the sequences in the knowledgebase. The alignment may be performed in polynomial time, regardless of the number of sequences that are aligned.

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.

Abstract: 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.

Abstract: A database system uses an iterative set to store data and relationships among the data in a parallel manner. Unlike a relational database, which is limited to representing two-dimensional relationships (i.e., relationships between pairs of tables), the database system of the present invention may represent N-dimensional relations in a three-dimensional coordinate system. Furthermore, the database system of the present invention may store all database data in a single iterative set, without the need to use multiple tables. As a result of the manner in which data and relationships among data are stored by embodiments of the present invention, embodiments of the present invention may be used to search the database without the need to formulate queries in a formal query language such as SQL.

Abstract: A nondeterministic Turing machine (NTM) performs computations 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 used to perform a variety of computational tasks, such as multiple sequence alignment, factorization, and other nondeterministic polynomial algorithms in polynomial time. The NTM may be constructed by a deterministic Turing machine (DTM) using the four systems listed above.

Abstract: A database system uses an iterative set to store data and relationships among the data in a parallel manner. Unlike a relational database, which is limited to representing two-dimensional relationships (i.e., relationships between pairs of tables), the database system of the present invention may represent N-dimensional relations in a three-dimensional coordinate system. Furthermore, the database system of the present invention may store all database data in a single iterative set, without the need to use multiple tables. As a result of the manner in which data and relationships among data are stored by embodiments of the present invention, embodiments of the present invention may be used to search the database without the need to formulate queries in a formal query language such as SQL.

Abstract: A nondeterministic Turning machine (NTM) performs computations 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 used to perform a variety of computational tasks, such as multiple sequence alignment, factorization, and other nondeterministic polynomial algorithms in polynomial time. The NTM may be constructed by a deterministic Turing machine (DTM) using the four systems listed above.

Abstract: A computer system aligns two or more sequences with each other to identify similarities and differences between the aligned sequences. The sequences may, for example, represent proteins. The system performs alignment quickly and accurately by representing the sequences as perceptual information and conceptual information having mappings between them in a knowledgebase, and then performing the alignment based on the representations of the sequences in the knowledgebase. The alignment may be performed in polynomial time, regardless of the number of sequences that are aligned.

Abstract: A computer system uses an inverse function method to solve Boolean Satisfiability problems. The system benefits from the system disclosed in the US patent “Knowledge Acquisition and Retrieval Apparatus and Method” (U.S. Pat. No. 6,611,841). The system applies a learning function to access iterative set relations among variables, literals, words and clauses as knowledge; and applies deduction and reduction functions to retrieve relations as reasoning. The system uses knowledge learning (KL) and knowledge reasoning algorithms (KRA). The system abandons the “OR” operation of Boolean logic and processes only set relations on data. The system leverages the reversibility of deduction and reduction to determine whether 3-SAT formulas are satisfiable.

Abstract: A computer system uses an inverse function method to solve Boolean Satisfiability problems. The system benefits from the system disclosed in the US patent “Knowledge Acquisition and Retrieval Apparatus and Method” (U.S. Pat. No. 6,611,841). The system applies a learning function to access iterative set relations among variables, literals, words and clauses as knowledge; and applies deduction and reduction functions to retrieve relations as reasoning. The system uses knowledge learning (KL) and knowledge reasoning algorithms (KRA). The system abandons the “OR” operation of Boolean logic and processes only set relations on data. The system leverages the reversibility of deduction and reduction to determine whether 3-SAT formulas are satisfiable.

Abstract: Disclosed is a knowledge reasoning method for solving Boolean Satisfiability problems. This method is one of the applications of the method disclosed in the US patent “Knowledge Acquisition and Retrieval Apparatus and Method” (U.S. Pat. No. 6,611,841). Disclosed method applies learning function to access iterative set relations among variables, literals, words and clauses as knowledge; And applies deduction and reduction functions to retrieve relations as reasoning. The process is a knowledge learning (KL) and knowledge reasoning algorithm (KRA). KRA abandons the “OR” operation of Boolean logic and processes only set relations of the data. The novelty of the disclosed method is the reversibility between the deduction and reduction. That is, KRA of Boolean Satisfiability applies a pair of perceptual-conceptual languages to learn member-class relations and retrieve information through deductive and reductive reasoning.

Abstract: A computer system represents numbers as three-dimensional relations, which may be represented as collections of points in three-dimensional space. The three-dimensional representations may use values of +1 and ?1 as complements of each other to overcome limitations of binary representations which use values of 1 and 0 to represent numbers. The computer system may use such three-dimensional relations to perform arithmetic and to factorize numbers.

Abstract: Disclosed is a knowledge reasoning method for solving Boolean Satisfiability problems. This method is one of the applications of the method disclosed in the US patent “Knowledge Acquisition and Retrieval Apparatus and Method” (U.S. Pat. No. 6,611,841). Disclosed method applies learning function to access iterative set relations among variables, literals, words and clauses as knowledge; And applies deduction and reduction functions to retrieve relations as reasoning. The process is a knowledge learning (KL) and knowledge reasoning algorithm (KRA). KRA abandons the “OR” operation of Boolean logic and processes only set relations of the data. The novelty of the disclosed method is the reversibility between the deduction and reduction. That is, KRA of Boolean Satisfiability applies a pair of perceptual-conceptual languages to learn member-class relations and retrieve information through deductive and reductive reasoning.

Abstract: Disclosed is a method for factoring integers by squaring computation time. The present invention uses binary numbers to process invert function of multiplication as factorization. Inverse method of integer factorization uses a diamond expansion form to arrange the digit positions of 1-numbers and 0-numbers subtracted from the product number P and its complement number No. The complement number N0 is the difference between the product number P and the square of the whole-1-number 1n2. The square of the whole-1-number 1n2 equals to the number of that first n-1 digits are 1s, followed by n 0s, and ended by 1.

Abstract: A system and method to organize information on the internet for rapid and organized retrieval. Registrants of websites can register URLs by specifying the URL and associated descriptors. A bot automatically determines URLs and metadata associated with the registered URL. The URLs and descriptors and/or metadata form a URL database. Search terms entered by users can be indexed against a knowledge database using one or more retrieval algorithms to provide keyword associations. The knowledge database further includes a knowledge acquisition and retrieval system and method that include at least one first memory segment, and a distinct second memory segment, wherein elements of the at least one first memory segment reciprocally associate to elements of the second memory segment. Registrants can modify the knowledge database to incorporate non-traditional associations.

Abstract: A method for associating data, including creating reciprocal associations between elements of at least one first memory segment and elements of at least one distinct second distinct memory segment to provide: (i) a hierarchical relationship between elements of the at least one first memory segment by traversing the reciprocal associations, and, (ii) a hierarchical relationship between elements of the at least one distinct second memory segment by traversing the reciprocal associations.

Abstract: A knowledge acquisition and retrieval apparatus and method that emulate the human brain and comprise at least one first memory segment, and a distinct second memory segment, wherein elements of the at least one first memory segment are reciprocally associated to elements of the second memory segment, and vice-versa. The at least one first memory segment comprises categorized data from the physical world, known as representational data, while the second memory segment contains abstract or conceptual data, otherwise known as consciousness data. Physical data comprises auditory data, language data, visual data, motion data, and sensory data, and each element of the at least one first memory segment is identified as auditory data, language data, visual data, motion data, or sensory data. By reciprocally associating the physical (representational) and conceptual (consciousness) data, a hierarchical structure is created that allows information retrieval by traversing the reciprocal associations.

Abstract: A system and method to organize information on the internet for rapid and organized retrieval. Registrants of websites can register URLs by specifying the URL and associated descriptors. A bot automatically determines URLs and metadata associated with the registered URL. The URLs and descriptors and/or metadata form a URL database. Search terms entered by users can be indexed against a knowledge database using one or more retrieval algorithms to provide keyword associations. The knowledge database further includes a knowledge acquisition and retrieval system and method that include at least one first memory segment, and a distinct second memory segment, wherein elements of the at least one first memory segment reciprocally associate to elements of the second memory segment. Registrants can modify the knowledge database to incorporate non-traditional associations.