On synthesis of easily testable (k, K) circuits

A (k, K) circuit is one which can be decomposed into nonintersecting blocks of gates where each block has no more than K external inputs, such that the graph formed by letting each block be a node and inserting edges between blocks if they share a signal line, is a partial k-tree. (k, K) circuits are special in that they have been shown to be testable in time polynomial in the number of gates in the circuit, and are useful if the constants k and K are small. We demonstrate a procedure to synthesise (k, K) circuits from a special class of Boolean expressions.