Finite State Model and Compatibility Theory: New Analysis Tools for Permutation Networks

In this paper, we present a new model, finite permutation machine (FPM), to describe the permutation networks. A set of theorems are developed to capture the theory of operations for the permutation networks. Using this new framework, an interesting problem is attacked: are 2n − 1 passes of shuffle exchange necessary and sufficient to realize all permutations? where n = log2 N and N is the number of inputs and outputs interconnected by the network. We prove that to realize all permutations, 2n − 1 passes of shuffle exchange are necessary and that 3n − 3 passes are sufficient. This reduces the sufficient number of passes by 2 from the best-known result.