D. V. Demidov

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 This paper deals with a method of relational theory adaptation for integrated circuits CAD systems. A new algorithm is worked out for optimal search of implicit Don’t Care values for combinational multiple-level digital circuits. The algorithm is described in terms of the adapted relational theory that gives the possibility for a very simple algorithm description for both intuitive understanding and formal analysis. The proposed method makes it possible to apply progressive experience of relational databases in efficient implementation of relational algebra operations (including distributed ones).  Comparative analysis of the proposed algorithm and a classic one for optimal search of implicit Don’t Cares is carried out. The analysis has proved formal correctness of the proposed algorithm and its considerably less worst-case complexity.  The search of implicit Don’t Care values in the integrated circuits design makes it easier to optimize such characteristics of IC as chip area, power, verifiability and reliability. However, the classic algorithm for optimal search of implicit Don’t Care values is not used in practice due to its very high computational complexity. Application of algorithms for sub-optimal search doesn’t give the possibility to realize the potential of IC optimization to the full. Implementation of the proposed algorithm in IC CAD (a.k.a., EDA) systems is adequate due to much lower computational complexity, and potentially makes it possible to improve the quality-development time ratio of IC (chip area, power, verifiability and reliability). Developed method gives the possibility for creation of distributed EDA system with higher computational power and, consequently, for design automation of more complex IC.

Keywords:  CAD, EDA, VLSI, optimization of combinational schemes, Boolean networks, partially defined Boolean functions, implicit Don’t Cares, ODC, relational theory, relational algebra, natural join

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