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: 1-81. (canceled) 82. A method of processing data, the method comprising: receiving, by a data processor comprising hardware, a data system comprising an aggregate of data units that manifest, as a whole, a state comprised by a state superset that comprises: different states of the data system, or a systemic characteristic of the data system, or both different states of the data system and the systemic characteristic of the data system, the data system corresponding to at least one of: an encoded message comprising symbols, a compressed message comprising bits, a document comprising graphemes or alphanumeric symbols, a digital picture comprising pixels, a waveform file comprising samples, a video file comprising picture frames, or an executable comprising machine code symbols; determining, by the data processor, probabilities of a plurality of different states of the data system or the systemic characteristic comprised by the state superset based at least in part on a spatial statistical model comprising an element that represents the state comprised by the state superset; constructing, by the data processor, a compressed message comprising an ordered list of identifiers based, at least in part, on a probability of the state of the data system or the systemic characteristic, the ordered list of identifiers representing at least one of the following: a boundary of a state subset, the state subset comprising a subset of states within the state superset, or a state of the data system or the systemic characteristic comprised by the state subset, or the state of the data system or the systemic characteristic comprised by the state superset, wherein, on average, a number of bits needed to construct the compressed message comprising the ordered list of identifiers is less than a number of bits needed to communicate the data system or the systemic characteristic in un-compressed form; configuring, by the data processor, a decoder to generate a generated data system that corresponds to the state of the data system or the systemic characteristic by providing the compressed message comprising the ordered list of identifiers to the decoder; generating, by the decoder, the generated data system based, at least in part, on the compressed message comprising the ordered list of identifiers. 83. The method of claim 82, further comprising determining, by the data processor, a number of possible states comprised by the state subset. 84. The method of claim 82, further comprising identifying, by the data processor, the state comprised by the state subset by employing a positional notation. 85. The method of claim 82, wherein determining the probabilities of the plurality of different states of the data system or the systemic characteristic, further comprises: initiating, by the data processor, a sequence function that operates on an ordered sequence of data units from the data system to generate an output sequence that corresponds to the ordered sequence; corresponding, by the data processor, the output sequence to the element that represents the state comprised by the state superset to determine, by the data processor, an argument value that enables the decoder to determine the probability of the state of the data system or the state of the systemic characteristic by employing a function that performs at least one of the following tasks: determining, by the data processor, a number of times the state of the data system or the systemic characteristic corresponds to the element; determining, by the data processor, a number of times a member of the output sequence corresponds to the element; determining, by the data processor, a probability of the state of the data system or the systemic characteristic corresponding to the element; determining, by the data processor, a range of probable sums of the ordered sequence of data units from the data system; selecting, by the data processor, the element as a constraint element representing the boundary of the state subset; determining, by the data processor, a probability distribution indicating the probability of the state of the data system or the systemic characteristic corresponding to the element; or determining, by the data processor, an indicator representing a type of state subset; and determining, by the data processor, a reference enabling an assignment of the probability of the state of the data system or the systemic characteristic corresponding to the element; constructing, by the data processor, the argument value; configuring, by the data processor, the decoder to determine the probability of the state of data system or the state of the systemic characteristic by at least providing the argument value to the decoder. 86. The method of claim 82, further comprising supercorresponding, by the data processor, at least two states of the state superset to a mutual element comprised by a space. 87. The method of claim 82, wherein the element corresponds to a location in space, wherein the space is selected from the group consisting of a Euclidean space, a Non-Euclidean space, a topological space and a phase space comprising at least one dimension. 88. The method of claim 82, further comprising constructing, by the data processor, a tree data structure comprising at least one of the following: an index comprising a number of occurring transformation cycles, a node that represents an appending of at least two separate data systems as an appended data system in the transformation cycles. 89. The method of claim 82, further comprising iteratively applying, by the data processor, in a generation cycle: receiving an ordered list of identifiers and generating a generated data system based, at least in part, on the received ordered list of identifiers. 90. The method of claim 82, further comprising matching, by the data processor, a current state of the data system or the systemic characteristic to a state of a known data system or the systemic characteristic comprised by a known state superset to recognize the current state of the data system or the systemic characteristic as being similar to the state of the known data system or the systemic characteristic. 91. The method of claim 82, wherein the state of the state subset or the state of the systemic characteristic corresponds to a random-like state. 92. A system comprising: a data store configured to store computer-executable instructions; and a hardware processor in communication with the data store, the hardware processor, configured to execute the computer-executable instructions to at least: receive a data system comprising an aggregate of data units that manifest, as a whole, a state comprised by a state superset that comprises: different states of the data system, or a systemic characteristic of the data system, or both different states of the data system and the systemic characteristic of the data system, the data system corresponding to at least one of: an encoded message comprising symbols, a compressed message comprising bits, a document comprising graphemes or alphanumeric symbols, a digital picture comprising pixels, a waveform file comprising samples, a video file comprising picture frames, or an executable comprising machine code symbols; determine probabilities of a plurality of different states of the data system or the systemic characteristic comprised by the state superset based at least in part on a spatial statistical model comprising an element that represents the state comprised by the state superset; construct a compressed message comprising an ordered list of identifiers based, at least in part, on a probability of the state of the data system or the systemic characteristic, the ordered list of identifiers representing at least one of the following: a boundary of a state subset, the state subset comprising a subset of states within the state superset, or a state of the data system or the systemic characteristic comprised by the state subset, or the state of the data system or the systemic characteristic comprised by the state superset; enable a decoder to generate a generated data system that corresponds to the state of the data system or the systemic characteristic by providing the compressed message comprising the ordered list of identifiers to the decoder. 93. The system of claim 92, wherein the system is configured to determine a number of possible states comprised by the state subset. 94. The system of claim 92, wherein the system is configured to identify the state comprised by the state subset by employing a positional notation. 95. The system of claim 92, wherein the determination of the probabilities of the plurality of different states of the data system or the systemic characteristic, further comprises: initiation of a sequence function that operates on an ordered sequence of data units from the data system to generate an output sequence that corresponds to the ordered sequence; correspondence of the output sequence to the element that represents the state comprised by the state superset to determine an argument value that enables the decoder to determine the probability of the state of the data system or the state of the systemic characteristic by employing a function that performs at least one of the following tasks: determination of a number of times the state of the data system or the systemic characteristic corresponds to the element; determination of a number of times a member of the output sequence corresponds to the element; determination of a probability of the state of the data system or the systemic characteristic corresponding to the element; determination of a range of probable sums of the ordered sequence of data units from the data system; selection of the element as a constraint element representing the boundary of the state subset; determination of a probability distribution indicating the probability of the state of the data system or the systemic characteristic corresponding to the element; determination of an indicator representing a type of state subset; or determination of a reference enabling an assignment of the probability of the state of the data system or the systemic characteristic corresponding to the element; construction of the argument value; configuration of the decoder to determine the probability of the state of data system or the state of the systemic characteristic by at least providing the argument value to the decoder. 96. The system of claim 92, wherein the system is configured to supercorrespond at least two states of the state superset to a mutual element comprised by a space. 97. The system of claim 92, wherein the element corresponds to a location in space, wherein the space is selected from the group consisting of a Euclidean space, a Non-Euclidean space, a topological space and a phase space comprising at least one dimension. 98. The system of claim 92, wherein the system is configured to construct a tree data structure comprising at least one of the following: an index comprising a number of occurring transformation cycles, a node that represents an appending of at least two separate data systems as an appended data system in the transformation cycles. 99. The system of claim 92, wherein the system is configured to iteratively apply in a generation cycle: receiving an ordered list of identifiers and generating a generated data system based, at least in part, on the received ordered list of identifiers. 100. The system of claim 92, wherein the system is configured to match a current state of the data system or the systemic characteristic to a state of a known data system or the systemic characteristic comprised by a known state superset to recognize the current state of the data system or the systemic characteristic as being similar to the state of the known data system or the systemic characteristic. 101. The system of claim 92, wherein the state of the state subset or the state of the systemic characteristic corresponds to a random-like state. 102. A method of processing data, the method comprising: receiving, by a data processor comprising hardware, a data system comprising an aggregate of data units that manifest, as a whole, a state comprised by a state superset that comprises: different states of the data system, or a systemic characteristic of the data system, or both different states of the data system and the systemic characteristic of the data system, the data system corresponding to at least one of: an encoded message comprising symbols, a compressed message comprising bits, a document comprising graphemes or alphanumeric symbols, a digital picture comprising pixels, a waveform file comprising samples, a video file comprising picture frames, or an executable comprising machine code symbols; determining, by the data processor, probabilities of a plurality of different states of the data system or the systemic characteristic comprised by the state superset based at least in part on a spatial statistical model comprising an element that represents the state comprised by the state superset; constructing, by the data processor, a compressed message comprising an ordered list of identifiers based, at least in part, on a probability of the state of the data system or the systemic characteristic, the ordered list of identifiers representing at least one of the following: a boundary of a state subset, the state subset comprising a subset of states within the state superset, or a state of the data system or the systemic characteristic comprised by the state subset, or the state of the data system or the systemic characteristic comprised by the state superset; enabling, by the data processor, a decoder to generate a generated data system that corresponds to the state of the data system or the systemic characteristic by providing the compressed message comprising the ordered list of identifiers to the decoder. 103. The method of claim 102, further comprising determining, by the data processor, a number of possible states comprised by the state subset. 104. The method of claim 102, further comprising identifying, by the data processor, the state comprised by the state subset by employing a positional notation. 105. The method of claim 102, wherein determining the probabilities of the plurality of different states of the data system or the systemic characteristic, further comprises: initiating, by the data processor, a sequence function that operates on an ordered sequence of data units from the data system to generate an output sequence that corresponds to the ordered sequence; corresponding, by the data processor, the output sequence to the element that represents the state comprised by the state superset to determine, by the data processor, an argument value that enables the decoder to determine the probability of the state of the data system or the state of the systemic characteristic by employing a function that performs at least one of the following tasks: determining, by the data processor, a number of times the state of the data system or the systemic characteristic corresponds to the element; determining, by the data processor, a number of times a member of the output sequence corresponds to the element; determining, by the data processor, a probability of the state of the data system or the systemic characteristic corresponding to the element; determining, by the data processor, a range of probable sums of the ordered sequence of data units from the data system; selecting, by the data processor, the element as a constraint element representing the boundary of the state subset; determining, by the data processor, a probability distribution indicating the probability of the state of the data system or the systemic characteristic corresponding to the element; determining, by the data processor, an indicator representing a type of state subset; or determining, by the data processor, a reference enabling an assignment of the probability of the state of the data system or the systemic characteristic corresponding to the element; constructing, by the data processor, the argument value; configuring, by the data processor, the decoder to determine the probability of the state of data system or the state of the systemic characteristic by at least providing the argument value to the decoder. 106. The method of claim 102, further comprising supercorresponding, by the data processor, at least two states of the state superset to a mutual element comprised by a space. 107. The method of claim 102, wherein the element corresponds to a location in space, wherein the space is selected from the group consisting of a Euclidean space, a Non-Euclidean space, a topological space and a phase space comprising at least one dimension. 108. The method of claim 102, further comprising constructing, by the data processor, a tree data structure comprising at least one of the following: an index comprising a number of occurring transformation cycles, a node that represents an appending of at least two separate data systems as an appended data system in the transformation cycles. 109. The method of claim 102, further comprising matching, by the data processor, a current state of the data system or the systemic characteristic to a state of a known data system or the systemic characteristic comprised by a known state superset to recognize the current state of the data system or the systemic characteristic as being similar to the state of the known data system or the systemic characteristic. 110. The method of claim 102, wherein the state of the state subset or the state of the systemic characteristic corresponds to a random-like state. 111. A non-transitory computer-readable storage medium storing computer-executable instructions that when executed by a processor perform operations comprising: receiving a data system comprising an aggregate of data units that manifest, as a whole, a state comprised by a state superset that comprises: different states of the data system, or a systemic characteristic of the data system, or both different states of the data system and the systemic characteristic of the data system, the data system corresponding to at least one of: an encoded message comprising symbols, a compressed message comprising bits, a document comprising graphemes or alphanumeric symbols, a digital picture comprising pixels, a waveform file comprising samples, a video file comprising picture frames, or an executable comprising machine code symbols; determining probabilities of a plurality of different states of the data system or the systemic characteristic comprised by the state superset based at least in part on a spatial statistical model comprising an element that represents the state comprised by the state superset; constructing a compressed message comprising an ordered list of identifiers based, at least in part, on a probability of the state of the data system or the systemic characteristic, the ordered list of identifiers representing at least one of the following: a boundary of a state subset, the state subset comprising a subset of states within the state superset, or a state of the data system or the systemic characteristic comprised by the state subset, or the state of the data system or the systemic characteristic comprised by the state superset; enabling a decoder to generate a generated data system that corresponds to the state of the data system or the systemic characteristic by providing the compressed message comprising the ordered list of identifiers to the decoder.