Transparallel processing

Transparallel processing is a form of processing, in computing or otherwise, in which items are processed simultaneously by one processor, that is, in one go, as if only one item were concerned.
Transparallel processing complements the three forms of processing called:
* subserial processing, in which items are processed one after the other by many processors;
* serial processing, in which items are processed one after the other by one processor;
* parallel processing, in which items are processed simultaneously by many processors.
Various everyday situations involve some combination of the latter three forms of processing. For instance, at the checkout in a supermarket, the cashiers work in parallel, but each cashier serially processes customer carts that are presented subserially by the customers.
Compared to subserial processing and serial processing, both parallel processing and transparallel processing imply a reduction in the amount of time needed to process all items. Transparallel processing implies, in addition, a reduction in the total amount of work to be done.
For instance, to select the longest pencil from among a number of pencils, the lengths of the pencils could be measured serially by one person, or subserially or in parallel by many persons. The parallel method is faster than the serial and subserial methods, but still involves the same amount of work. The following transparallel method, however, is both time-efficient and work-efficient: One person gathers all pencils in a bundle and places the bundle upright on a table, so that the longest pencil can be selected in a glance.
Transparallel processing in computers
Transparallel processing is the extraordinarily powerful form of processing promised by quantum computers. Furthermore, although a single-processor classical computer cannot perform parallel processing, 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 candidate interpretations of 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(2 ) strings, which is such that the O(2 ) strings can be searched for regularities as if only one string of length N were concerned. Hence, the O(2 ) 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.

In other words, whereas quantum computers provide a hardware solution to perform transparallel processing (for some computing problems), hyperstrings provide a software solution to perform transparallel processing on single-processor classical computers (for at least one computing problem).
Transparallel processing in the brain
Visually relevant regularities are regularities the brain is attuned to. Considering that these regularities lend themselves for transparallel processing in computers, transparallel processing might also be a form of processing in the brain — as expressed in the transparallel mind hypothesis.
The brain is a network consisting of many interconnected neurons which can be said to process biochemical information. A growing body of evidence, however, suggests that cognitive information processing is mediated by transient assemblies of neurons, which signal their presence by synchronous firing of the neurons involved. This neural synchronization is required neither for (sub)serial processing nor for parallel processing, but might be a manifestation of transparallel processing mediated by those neural assemblies. These assemblies can be seen as neural analogues of hyperstrings and might be the constituents of flexible cognitive architecture implemented in the brain.

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