Transparallel Processing in Computers
A single computer processor cannot perform parallel processing, but it can perform transparallel processing. This was found in, and is illustrated by the following example from, structural information theory which is a computational Gestalt theory about visual form perception that models percepts by simplest hierarchical codes (i.e., most compact descriptions) of symbol strings representing visual stimuli.
To select a simplest code from among all possible codes of a string, the string is searched for visually relevant regularities such as symmetry and repetition. This search gives rise to numerous strings representing hierarchical levels in possible codes. These strings all are to be searched for regularities too. By nature, however, these strings group into so-called hyperstrings. A hyperstring is a distributed representation of O(2N) strings, which is such that the O(2N) strings can be searched for regularities as if only one string of length N were concerned. Hence, the O(2N) strings neither have to be searched for regularities in a subserial or serial fashion (i.e., one string after the other) nor in a parallel fashion (i.e., simultaneously by many processors), but they can be searched for regularities in a transparallel fashion (i.e., simultaneously by one processor).
Hyperstrings. Each of the 15 paths from vertex 1 to vertex 9 in this hyperstring represents a string. In graph-theoretical terms, a hyperstring is a simple semi-Hamiltonian directed acyclic graph with the following property: Let π(v1,v2) be the set of substrings represented by the paths from vertex v1 to vertex v2; then, for all i, j, p, q, two substring sets π(i,j) and π(p,q) are either identical or disjunct. Here, for instance, π(1,4) and π(5,8) are identical substring sets containing the substrings abc, xc, and ay. This property enables the 15 strings to be searched for regularities in a transparallel fashion, that is, as if only one string were concerned.
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