Lattice-based computation of boolean functions

Abstract

This paper studies the implementation of Boolean functions with lattices of two-dimensional switches. Each switch is controlled by a Boolean literal. If the literal is 1, the switch is connected to its four neighbours; else it is not connected. Boolean functions are implemented in terms of connectivity across the lattice: a Boolean function evaluates to 1 iff there exists a top-to-bottom path. The paper addresses the following synthesis problem: how should we map literals to switches in a lattice in order to implement a given target Boolean function? We seek to minimize the number of switches. Also, we aim for an efficient algorithm - one that does not exhaustively enumerate paths. We exploit the concept of lattice and Boolean function duality. We demonstrate a synthesis method that produces lattices with a number of switches that grows linearly with the number of product terms in the function. Our algorithm runs in time that grows polynomially.