Within the combinatorial framework we develop, our first application is in deriving combinatorial conditions, involving the transfer parameters, which precisely delimit the boundary between counting networks and sorting networks. The sufficiency of the shown combinatorial conditions is employed in designing the first formal algorithms for mathematically verifying that a given network belongs to each of a collection of classes. These algorithms are simple, modular and easy to implement, consisting merely of multiplying matrices and evaluating matricial functions. The abstract is also available as a LaTeX file , a DVI file , or a PostScript file . A combinatorial treatment of balancing networks.
Impossibility results for weak threshold networks.
Selected references James Aspnes, Maurice Herlihy, and Nir Shavit. James Aspnes, Maurice Herlihy, and Nir Shavit. Counting networks and multi-processor coordination. Martin Dowd, Yehoshua Perl, Larry Rudolph, and Michael Saks. The periodic balanced sorting network.