A Residue Number System on Reconfigurable Mesh with Applications to Prefix Sums and Approximate String Matching

ÐSeveral new number representations based on a Residue Number System are presented which use the smallest prime numbers as moduli and are suited for parallel computations on a reconfigurable mesh architecture. The bit model of linear reconfigurable mesh with exclusive write and unit-time delay for broadcasting on a subbus is assumed. It is shown how to convert in O…1† time any integer, ranging between 0 and nÿ 1, from any commonly used representation to any new representation proposed in this paper (and vice versa) using an n O log n log logn reconfigurable mesh. In particular, some of the previously known conversion techniques are improved. Moreover, as a byproduct, it is shown how to compute in O…1† time the Prefix Sums of n bits by a reconfigurable mesh having the above mentioned size, thus improving previously known results. Applications to the Prefix Sums of N h-bit integers and to Approximate String Matching with mismatches are also considered. The Summation and the Prefix Sums can be computed in O…1† time using O h logN ‡ log N log logN Nh and O h2‡log2 N log…h‡logN† O…N…h‡ logN†† reconfigurable meshes, respectively. Moreover, it is shown for the first time how to find in O…1† time all the occurrences of a pattern of length m in a text of length n, allowing less than mismatches, using a reconfigurable mesh of size O…m log j j† O n log j j ‡ log log log , where the pattern and the text are strings over a finite alphabet and < m n. Index TermsÐNumber representation, prefix sums, reconfigurable mesh, residue number system, string matching with k mismatches,