A hardware sorter suitable for VLSI implementation is proposed. I t operates in a parallel and pipelined fashion, with the actual sorting time absorbed by the inputloutput time. A detailed VLSI implementation is described which has a very favorable device count compared to existing static RAM. 1. Introduction Sorting is one of the most important operations in data while the item at the top cell...

Each relational structure X has an associated Gaifman graph, which endows X with the properties of a graph. If x is an element of X, let Bn(x) be the ball of radius n around x. Suppose that X is infinite, connected and of bounded degree. A first-order sentence φ in the language of X is almost surely true (resp. a.s. false) for finite substructures of X if for every x ∈ X, the fraction of substr...

Abstract Let $$n \ge 4$$ n ≥ 4 be a positive integer, $$\mathcal {F}$$ F family of meromorphic functions in D and let $$a(z)(\not \equiv 0), b(z)$$ a ( z ) ≢</m...

Convergence is proven for the mass zero cluster expansion presented in Part 1 of this paper. An indication is given of changes necessary to treat the more difficult 2(V~b) 4 model and the lattice dipole gas. 9. Counting I In these sections we will be concerned with enumerating the terms in the cluster expansion in a way suitable for estimation. The complexities are largely notational, and due t...