A residue number system on reconfigurable mesh with applications to prefix sums and approximate string matching

Several 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 n-1, from any commonly used representation to any new representation proposed in this paper (and vice versa) using an n×O(log² n/log log n) 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 α mismatches are also considered. The Summation and the Prefix Sums can be computed in O(1) time using O(h log N+log² N/log log N)×Nh and O(h²+log² N/log(h+log N))×O(N(h+log N)) 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 α mismatches, using a reconfigurable mesh of size O(m log|Σ|)×O (n(log|Σ|+log² α/log log α)), where the pattern and the text are strings over a finite alphabet Σ and α\n\n\t\t