Advanced Symbolic Analysis for VLSI Systems: Methods and by Guoyong Shi, Sheldon X.-D. Tan, Esteban Tlelo Cuautle

By Guoyong Shi, Sheldon X.-D. Tan, Esteban Tlelo Cuautle (auth.)

This booklet offers complete assurance of the hot advances in symbolic research strategies for layout automation of nanometer VLSI platforms. The presentation is geared up in components of basics, uncomplicated implementation equipment and functions for VLSI layout. issues emphasised comprise statistical timing and crosstalk research, statistical and parallel research, functionality sure research and behavioral modeling for analog built-in circuits. one of the contemporary advances, the Binary choice Diagram (BDD) established techniques are studied extensive. The BDD-based hierarchical symbolic research ways, have basically damaged the analog circuit measurement barrier.

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This method has several limitations as pointed out later by the work [200] in 2010. Such limitations can be improved by adopting a new implementation taking the advantage of object-based sharing. , sub-determinant) can be uniquely identified by the row and column indexes provided that the nonzeros of the original full dimensional matrix has been ordered. This basic proposition guarantees that the BDD constructed by using minor-based sharing be automatically minimal. One thing that requires special attention in algebraic BDD is that there could be some BDD nodes whose solid arrows point to the terminal “0”.

The reader is referred to [13] for the details of implementation in this regard. The triple-based sharing is also employed for reducing a non-canonical BDD to be canonical. In case a BDD is constructed without the assurance of canonicity, one may run a Reduce procedure from bottom up to enforce the canonicity [15]. What it is done in the Reduce procedure is just to re-identify the sharable triples and reconnect some decision arrows. After the Reduce procedure, redundant sub-BDDs would be produced whose roots are not referenced (or pointed) by any other BDD arrows.

Det(A) (13) 20 2 Symbolic Analysis Techniques in a Nutshell where Ak denotes the n × n matrix A whose kth column has been replaced by the column b. The Cramer’s rule tells us that any unknown x1 , . . , xn can be solved explicitly as a ratio of two determinants. If we expand the determinant det(Ak ) along the kth column, then the unknown xk can be expressed in the following form xk = n i=1 bi (−1)i+k det(Aai,k ) , det(A) (14) where det(Aai,k ) is the minor of det(A) with respect to element ai,k , called a firstorder minor.

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