A Combinatorial Characterization of Properties Preserved by Antitokens

Introduction Balancing networks were devised by Aspnes et al. [4] as a novel class of distributed data structures that provide highly-concurrent, low-contention solutions to a varietyofmultiprocessor synchronization problems. A balancing network is constructed from elementary switches with # input wires and # output wires, called (## #)-balancers. A (## #)-balancer accepts a stream of tokens on its # input wires. The #-th token to enter the balancer leaves on output wire # mod #, where # =0# 1####. One can think of a balancer as having a \toggle" state variable tracking which output wire the next token should exit from. A token traversal amounts to a Fetch&Increment operation to the toggle variable. This operation includes reading the current state of the toggle