Show that the Odd Even network in Fig.12.28 is a sorting network but not a counting network. Can counting networks do anything besides increments? Consider a new kind of token, called an anti token,...

Show that the Odd Even network in Fig.12.28 is a sorting network but not a counting network.

Can counting networks do anything besides increments? Consider a new kind of token, called an anti token, which we use for decrements. Recall that when a token visits a balancer, it executesget And Complement(): It atomically reads the toggle value and complements it, and then departs on the output wire indicated by the old toggle value. Instead, an anti token complements the toggle value, and then departs on the output wire indicated by the new toggle value. Informally, an anti token“ cancels” the effect of the most recent token on the balancer’s toggle state, and vice versa.