Massively parallel fault tolerant computations on syntactical patterns

The general capabilities of reliable computations in linear cellular arrays are investigated in terms of syntactical pattern recognition. We consider defects of the processing elements themselves and defects of their communication links, In particular, a processing element (cell) is assumed to behave as follows. Dependent on the result of a self-diagnosis it stores its working state locally such that it becomes visible to the neighbors. A defective cell cannot modify information but is able to transmit it unchanged with unit speed. Cells with link failures are not able to receive information via at most one of their both links to adjacent cells. Moreover, static and dynamic defects are distinguished. It is shown that fault tolerant real-time recognition capabilities of two-way arrays with static defects are characterizable by intact one-way arrays and that one-way arrays are fault tolerant per se. For arrays with dynamic defects it is proved that all failures can be compensated as long as the number of adjacent defective cells is bounded. In case of arrays with link failures it is shown that the sets of patterns that are reliably recognizable are strictly in between the sets of (intact) one-way and (intact) two-way arrays. (C) 2002 Published by Elsevier Science B.V.