We formalize the construction of Paterson’s variant of the Ajtai–Koml´os–Szemer´edi sorting network of logarithmic depth in the bounded arithmetical theory VNC1 ∗ (an ex...
Abstract. Correction networks are comparator networks that sort inputs differing from sorted sequences of length N in a small number of positions. The main application of such netw...
Hypercubic sorting networks are a class of comparator networks whose structure maps e ciently to the hypercube and any of its bounded degree variants. Recently, n-input hypercubic...
We study families of Boolean circuits with the property that the number of gates at distance t fanning into or out of any given gate in a circuit is bounded above by a polynomial ...