Title :
Mathematical methods in VLSI
Author :
Atre, M.V. ; Subramanian, P.S. ; Narayanan, H.
Author_Institution :
Agere Syst., Lucent Technol., Bangalore, India
Abstract :
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
Keywords :
VLSI; application specific integrated circuits; circuit CAD; circuit simulation; integrated circuit design; integrated circuit modelling; symbol manipulation; VLSI; automation; behavioral decomposition; design flow; high complexity designs; mathematical methods; partitioning; problem domain; simulation; structural decomposition; symbolic reasoning; systems-on-chip; Automata; Circuit simulation; Context modeling; Design automation; Differential equations; Large-scale systems; Mathematical model; Mathematics; Physics; Very large scale integration;
Conference_Titel :
Design Automation Conference, 2002. Proceedings of ASP-DAC 2002. 7th Asia and South Pacific and the 15th International Conference on VLSI Design. Proceedings.
Conference_Location :
Bangalore
Print_ISBN :
0-7695-1441-3
DOI :
10.1109/ASPDAC.2002.994876