All Around Logic Synthesis

This dissertation is in the area of Computer-Aided Design (CAD) of digital Integrated Circuits (ICs). Today’s digital ICs, such as microprocessors, memories, digital signal processors (DSPs), etc., range from a few thousands to billions of logic gates, flip-flops, and other components, packed in a few millimeters of area. The creation of such highly complex systems would not be possible without the use of CAD tools. CAD tools play the key role in determining the area, speed and power consumption of the resulting circuits. We address several problems related to the logic synthesis step of the CAD flow. First, we investigate properties of double-vertex dominators in directed acyclic graphs. We present an O(n) algorithm for identifying all O(n2) double-vertex dominators of a given vertex, where n is the size of the graph. The key to the algorithm’s efficiency is a new data structure for representing double-vertex dominators which has O(n) size and can be efficiently manipulated. This work improves the state of the art in doublevertex dominators identification in terms of both space and time complexity. We also show how dominators can be used for structural decomposition of Boolean functions represented by circuit graphs. Next, we present a depth-optimal technology mapping algorithm for look-up table (LUT) based Field Programmable Gate Arrays. This algorithm is two orders of magnitude faster than previous technology mapping algorithms while achieving solution with a smaller number of LUTs. We also consider level-limited decomposition of Boolean functions which is of particular interest for applications which require circuit representations of a limited depth, such as control logic of microprocessors. We present an efficient algorithm for computing the decomposition of type f = g · h + r, where f ,g,h and r are Boolean functions. Another contribution of the dissertation is an algorithm for identifying and removing redundancy in combinational circuits. This algorithm provides a quick partial solution which might be more suitable than exact ATPG and SAT-based approaches for redundancy removal runs at the intermediate steps of the CAD flow. It is embedded into the internal logic synthesis tool of IBM. Other contributions of the dissertation are a proof that, for some Reduced Ordered Binary Decision Diagrams, none of the bound-set preserving orderings is best, a proof of the existence of a perfect input assignment which guarantees that two non-equivalent Boolean functions hash to two different values, and a set of efficient algorithms for the analysis of random Boolean networks.