A method, article comprising machine-readable instructions and apparatus that processes data systems for encoding, decoding, pattern recognition/matching and data generation is disclosed. State subsets of a data system are identified for the efficient processing of data based, at least in part, on the data system's systemic characteristics.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A system comprising: a processing device; a non-transitory, tangible medium that stores instructions that when executed by the processing device cause the system to perform operations comprising: reducing memory and storage needed to determine a probability of states of a data system and/or a systemic characteristic of the data system by, at least: accessing a value corresponding to a point comprised by a plurality of points, the point and the plurality of points comprised by a space of a spatial probability model, the point corresponding to at least one state comprised by a state superset of at least one of the following: the data system or the systemic characteristic of the data system, the plurality of points comprising at least one supercorresponding point corresponding to at least two states of the state superset; determining a spatial probability model output based, at least in part, on the value corresponding to the point comprised by the space of the spatial probability model, the spatial probability model output corresponding to at least one of the following: a boundary of a state subset, the state subset comprising a subset of states of the state superset, or a spatial probability model value enabling a determination of a probability of the state comprised by the state superset of: the data system or the systemic characteristic of the data system; performing at least one of the following: generating data corresponding to a state comprised by the state subset based, at least in part, on the spatial probability model output, and storing, processing, and/or transmitting the generated data, or analyzing the spatial probability model output, generating corresponding analyzed data and storing, processing, and/or transmitting the analyzed data, or generating forecasted data corresponding to the state comprised by the state subset based, at least in part, on the spatial probability model output, and storing, processing, and/or transmitting the forecasted data, or determining a match test output by determining if input data, or a portion thereof, corresponds to the state comprised by the state subset based, at least in part, on the spatial probability model output, and generating, using the match test output, corresponding output data, and storing, processing, and/or transmitting the output data, or a portion thereof. 2. The system of claim 1, the operations further comprising: receiving the data system; using a sequence function that operates on an ordered sequence of data units from the data system to generate an output sequence; corresponding the output sequence to the point comprised by the space of the spatial probability model by employing a function that at least: determines a number of times the state, comprised by the state superset of the data system or state superset of the systemic characteristic of the data system, corresponds to the point comprised by the space, or determines a number of times data units of the output sequence correspond to the point comprised by the space, or determines the spatial probability model value corresponding to the point comprised by the space, the point corresponding to the state, comprised by the state superset of the data system or the state superset of the systemic characteristic of the data system, or determines a range of probable sums of the ordered sequence of data units from the data system, or determines a probability distribution indicating the spatial probability model value corresponding to the state, comprised by the state superset of the data system or comprised by the state superset of the systemic characteristic of the data system, corresponding to the point comprised by the space, or determines an identifier representing a state subset type, or determines an identifier enabling an assignment of the spatial probability model value corresponding to the state, comprised by the state superset of the data system or comprised by the state superset of the systemic characteristic of the data system, corresponding to the point comprised by the space. 3. The system of claim 2, the operations further comprising generating a hierarchical multi-resolution structure corresponding to the space of the spatial probability model and/or the output sequence. 4. The system of claim 1, wherein the spatial probability model comprises at least a Euclidean space, a Non-Euclidean space, a topological space, or a phase space. 5. The system of claim 1, wherein the space of the spatial probability model comprises at least two dimensions. 6. The system of claim 1, the operations further comprising determining a location of the point comprised by the space of the spatial probability model in a continuous space. 7. The method of claim 1, wherein the spatial probability model value enables a determination of an indentation value that corresponds with the spatial probability model value of the state comprised by the state superset, the indentation value enabling a collision detector to determine a degree of collision between the input data and the indention value. 8. The method of claim 1, the operations further comprising: receiving an ordered list of identifiers representing the spatial probability model value and assigning the spatial probability model value to the point to the point comprised by the space of the spatial probability model. 9. The system of claim 1, wherein the state subset is determined based on at least probability constraints, probability distributions, probability distribution functions and/or probability mappings. 10. The system of claim 1, wherein the systemic characteristic of the data system corresponds to a structure, a unit of data, a data subsystem, a relationship between units or subsystems, a process, or a spatial form. 11. A method comprising: accessing, by a processing device, a value corresponding to a point comprised by a plurality of points, the point and the plurality of points comprised by a space of a spatial probability model, the point corresponding to at least one state comprised by a state superset of at least one of the following: the data system or the systemic characteristic of the data system, the plurality of points comprising at least one supercorresponding point corresponding to at least two states of the state superset; determining, by the, by the processing device, an output based at least in part on the value corresponding to the point comprised by the space of the spatial probability model, the output corresponding to at least one of the following: a boundary of a state subset, the state subset comprising a subset of states of the state superset, or a probability of the state comprised by the state superset of: the data system or the systemic characteristic of the data system; using the output corresponding to at least one of the boundary of the state subset or the probability of the state, to determine data with reduced information entropy when performing at least one of the following: generating data comprising and/or being similar to data with reduced average information entropy and storing and/or transmitting generated data, or generating an analysis of data, the analysis of data comprising and/or being similar to data with reduced average information entropy, or generating forecasted data comprising and/or being similar to data with reduced average information entropy and storing and/or transmitting the analysis of data and/or forecasted data. determining matched data that matches and/or is similar to input data, the matched data comprising and/or being similar to the data with reduced average information entropy, and storing and/or transmitting at least a portion of the data with reduced redundancy and/or reduced average information entropy. 12. The method of claim 11, further comprising: receiving, by the data processor, the data system; using, by the processing device, a sequence function that operates on an ordered sequence of data units from the data system to generate an output sequence; corresponding, by the processing device, the output sequence to an element of the spatial probability model by employing a function that at least: determines a number of times the state, comprised by the state superset of the data system or state superset of the systemic characteristic of the data system, corresponds to the point comprised by the space, or determines a number of times data units of the output sequence correspond to the point comprised by the space, or determines the spatial probability model value corresponding to the point comprised by the space, the point corresponding to the state, comprised by the state superset of the data system or the state superset of the systemic characteristic of the data system, or determines a range of probable sums of the ordered sequence of data units from the data system, or determines a probability distribution indicating the probability of the state, comprised by the state superset of the data system or comprised by the state superset of the systemic characteristic of the data system, corresponding to the point comprised by the space, or determines an identifier representing a state subset type, or determines an identifier enabling an assignment of the probability of the state, comprised by the state superset of the data system or comprised by the state superset of the systemic characteristic of the data system, corresponding to the point comprised by the space. 13. The method of claim 11, wherein the spatial probability model comprises at least a Euclidean space, a Non-Euclidean space, a topological space, or a phase space. 14. The method of claim 11, wherein the space of the spatial probability model comprises at least two dimensions. 15. The method of claim 12, the method further comprising implementing, by the processing device, a hierarchical multi-resolution structure for the space and/or the output sequence. 16. The method of claim 11, the method further comprising: receiving an ordered list of identifiers representing the spatial probability model value and assigning the spatial probability model value to the point comprised by the space of the spatial probability model. 17. The method of claim 12, wherein the sequence function comprises at least a mathematical monotonically increasing function, a summation function, a multiplication function, a delta function, a trigonometric function, a lexicographic ordering function, a sorting function, or a sequence function that generates a delta value of the output sequence that is a measure of a variance from a determined value. 18. The method of claim 11, wherein the spatial probability model value enables a determination of an indentation that corresponds with the probability of the state comprised by the state superset, the indentation enabling a collision detection test between the received input data and the spatial probability model out to determine how well the received input matches with the spatial probability model output. 19. The method of claim 11, the method further comprising determining a location of the point comprised by the space in a continuous space. 20. The method of claim 11, wherein the systemic characteristic of the data system corresponds to a structure, a unit of data, a data subsystem, a relationship between units or subsystems, a process, or a spatial form.