Method for solving frequency, frequency distribution and sequence-matching problems using multidimensional attractor tokens

A method for recognizing the identity of a family of permutations of a source multiset in a space of multisets containing combinations of set elements, repeat elements, and permutations of those combinations of set elements and repeat elements, said method comprising the steps of:

• a) configuring a device in at least one of hardware, firmware and software to carry out an attractor process for mapping said source multiset to an attractor space, said attractor process being an iterative process which causes said plurality of elements to converge on one of at least two different behaviors defined within said attractor space as a result of said iterative process, said configuring step including inputting a characterization of the source multiset to input to said device the number of distinct elements of said source multiset;
• b) using said device, executing said mapping of said plurality of elements, N, of said multiset to one or more coordinates in said attractor space;
• c) mapping said attractor space coordinates as part of an accumulation of attractor space coordinates into a target space representation, said target space representation including at least the attractor space coordinates, said target space being designed to provide representational structure to the accumulation of attractor space coordinates;
• d) removing one or more elements as a group from the source multiset to form a source multiset with N=N−1 element groups;
• e) repeating steps b), c) and d) until N is less than a pre-determined value;
• f) mapping said target space representation into an analytic space to determine the source multiset's combinatorial identity, said analytic space including at least the attractor space coordinate and an identification of said source multiset;
• g) storing a representation of said analytic space.

A method of sequence matching, comprising:

• mapping a plurality of sequences from an original representation space (ORS) comprised of sequences into a hierarchical multidimensional attractor behavior space (HMBS), to draw the sequences respectively to a plurality of attractor behaviors in the HMBS, wherein each of the attractor behaviors forms a unique identity for a given group of said sequences with no overlap between different groups of sequences represented by different attractor behaviors, then mapping the attractor identity to an analytical symbol that is part of an analytical symbol scheme;
• repeating the step of mapping a plurality of subsequences of a given one of the sequences to create a string of analytical symbols for the given sequence and the subsequences, the step of mapping the subsequences comprising repeatedly removing a sequence element from the first end of the given sequence, the resulting string of analytical symbols representing an exact identity of the given sequence and all of the subsequences ordered from the first end of the given sequence;
• repeating the step of mapping a plurality of subsequences of a given one of the sequences to create a string of analytical symbols for the given sequence and the subsequences, the step of mapping the subsequences comprising repeatedly removing a sequence element from the second end of the given sequence, the resulting string of analytical symbols representing an exact identity of the given sequence and all of the subsequences ordered from the second end of the given sequence;
• repeating the step of mapping a plurality of subsequences for each subsequence created above forming two groups of analytical symbol strings each composed of an analytical symbol sequence for the sequence and each subsequence with one group comprising those analytical symbol strings created by first end sequence element removal and the second group comprising those analytical symbol strings created by second end sequence element removal;
• mapping said groups of analytical symbol strings to create a series of spatial coordinates in a hierarchy of spaces;
• and
• evaluating sequence-similarity characteristics of at least two strings of analytical symbols on from the first end of the sequence in a space, a group of spaces or a hierarchy of spaces to compare at least two of the sequences.

A method of sequence matching comprising:

• a) mapping a first sequence having a plurality of sequence elements from an original representation space (ORS) into a multidimensional attractor behavior space (HMBS), said first sequence converging to one of at least two distinct behaviors in said attractor behavior space, wherein each behavior is assigned a unique analytical symbol from an analytical symbol scheme, such that the first sequence convergence and analytical symbol assignment is the first analytical symbol;
• b) forming a plurality of subsequences of said first sequence;
• and
• c) mapping said plurality of subsequences of said first sequence to said HMBS space to create a plurality of analytical symbols corresponding to the behavior of each subsequence, said first analytical symbol and said plurality of analytical symbols defining together a first analytical symbol string uniquely characterizing said first sequence including its subsequences;
• wherein the step of forming a plurality of subsequences comprising:
• 1) removing a sequence element from a first end of the first sequence to produce a subsequence;
• 2) iteratively repeating step 1) for the produced subsequence to form subsequent subsequences;
• 3) removing a symbol from a second end of the first sequence to produce another subsequence;
• 4) iteratively repeating step 3) for the produced subsequence to form subsequent other subsequences,
• d) ordering said first analytical symbol string to produce an ordered first analytical symbol string;
• and
• e) repeating steps a)-d) for a second sequence to obtain an ordered second analytical symbol string;
• f) said first and second analytical symbol string representing an exact identity of the first and second sequences respectively and all subsequences ordered from the first and second ends of the first and second sequences;
• and
• g) comparing the ordered first analytical symbol string with the ordered second analytical symbol string whereby a match may be detected between said first sequence and said second sequence.