Exact reliability evaluation of mesh-connected processors

An analytical model for estimating the exact reliability for mesh-connected processors is introduced. The model assumes perfect recognition of a submesh in a mesh, or equivalently recognizing a submesh if it actually exists in a mesh. It is concerned with making use of every available node that can help in recognizing a demanded submesh. It has been pointed out in previous researches that it is almost impossible to estimate the exact reliability for such a topology as the problem space is prohibitively large. Thus, attempts have been made to approximate matters by computing a lower bound value for the required reliability which affects the efficiency of the would-be-made decisions. In this work we solve the problem of estimating the exact reliability without any approximation. It is exceedingly better to say that the reliability is 0.75 rather than it cannot be less than 0.4. We introduce the concept of simplifying the successful instances of the status of the mesh for a required submesh into patterns which reduces the total number of computations needed. Reduction is again done by storing and restoring results which saves a considerable redundant number of computations. A special case of estimating the reliability of recognizing an (N×m) submesh in an (N×m) mesh is proposed. The estimation of the reliability in the general case of recognizing an (n×m) submesh in an (N×M) mesh follows