Applications of Decision Diagrams in Digital Circuit Design

Design methodology of digital circuits is a rapidly changing eld. In the last 20 years, the number of transistors on a single chip has increased from thousands to tens of millions. This sets new demands on the design tools involved, their ability to capture speci cations on a high level, and nally synthesize them into hardware implementations. The introduction of Decision Diagrams (DDs) has brought new means towards solving many of the problems raised by the increasing complexity of todays designs. In this thesis, we study their use in VLSI CAD and develop a number of novel applications. Incomplete speci cations are inherent to the functionality of almost all digital circuits. We present a design methodology providing a common basis between design validation and logic synthesis, namely the semantics of Kleenean Strong Ternary Logic. This is called upon as commonly used design methodologies, based e.g. on VHDL, are shown to put design correctness in jeopardy. By an extension of DDs, we can e ciently represent and manipulate incompletely speci ed functions. The method presented, not only guarantees correctness of the nal circuit, but also o ers potential towards expressing and utilizing incompleteness in ways other methodologies are incapable of. The increasing density and speed of todays target technologies also changes the conditions for logic synthesis; e.g., traditional quality measures based on gate delays are becoming less accurate as delays caused by interconnections are raising their heads. To address this problem we propose methodologies allowing quality measures of the nal circuit to be foreseen and considered throughout the whole synthesis process. In general this is a very hard task. We approach the problem by limiting our synthesis methodologies to those rendering regular layouts (such as computational arrays and lattices). The regularity allows us to predict properties of the nal circuit and at the same time, ensure design criteria to be met, e.g., path delays and routability of the nal circuit. In this thesis, we develop new design methodologies and their algorithms. By our experimental results, they are shown to o er signi cant improvements to both state of the art two-level and multi-level based tools in the area of layout driven synthesis. Our minimization methods are based on Pseudo Kronecker Decision Diagrams (PKDDs), which are the most general type of ordered bit-level diagrams for switching functions. In the thesis we elaborate on the properties of PKDDs and Ternary PKDDs (TPKDDs) and develop an e cient minimization method based on local variable exchange for TPKDDs. Furthermore, the problem of PKDD minimization is discussed and a number of di erent strategies are introduced and evaluated; the potential compactness of PKDDs is con rmed. The thesis spans from validation and veri cation of high-level speci cations all the way down to layout driven synthesis, combining logic minimization, mapping and routing to the target architecture at hand. We conclude our work to o er new means towards solving many of the crucial problems occurring along the design process of modern digital circuits.