Mathematical methods in VLSI

Summary form only given. The theme of the tutorial is the use of mathematical methods in VLSI. The traditional use of mathematics in engineering disciplines is via mathematical modeling - concepts and interactions in the problem domain are mapped to objects and relationships of a specific mathematical topic and then the formal deductions within the topic are re-interpreted in the problem domain. After a structured review of VLSI design flow and the identification of mathematical topics applicable to each step of the design flow, the tutorial illustrates these themes by a sampling of mathematical techniques applicable to analysis of modeling and simulation, partitioning, structural and behavioral decomposition, and symbolic reasoning about behavior. The tutorial is aimed at illustrating the importance of mathematics in VLSI, especially in the development of various tools, which are critical for design. The audience will be made to appreciate how some of the tools which are used by designers actually have some very deep mathematics built into them, without which it would be impossible for any automation in the design process. This mathematics becomes more important as we go to high complexity designs involving millions of transistors, high frequencies and systems-on-chip