By Guoyong Shi, Sheldon X.-D. Tan, Esteban Tlelo Cuautle (auth.)
This publication offers finished insurance of the hot advances in symbolic research concepts for layout automation of nanometer VLSI structures. The presentation is equipped in components of basics, uncomplicated implementation tools and functions for VLSI layout. subject matters emphasised contain statistical timing and crosstalk research, statistical and parallel research, functionality certain research and behavioral modeling for analog built-in circuits. one of the contemporary advances, the Binary selection Diagram (BDD) established methods are studied extensive. The BDD-based hierarchical symbolic research techniques, have basically damaged the analog circuit measurement barrier.
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Additional resources for Advanced Symbolic Analysis for VLSI Systems: Methods and Applications, 1st Edition
The main benefit of this method is that the number of samplings required for building the variation subspace can be much less than that of normal Monte Carlo samplings. However, this method is far from mature and many problems remain to be solved. For instance, how to select the best sampling set to minimize the computing cost and improve the accuracy of the reduced models still remains an open problem. 4 Mathematical Concepts and Notation Some basic mathematical concepts and notation, mainly in linear algebra, are summarized in this section for reference.
1 | = |π2 |. The square submatrix obtained from the matrix A by retaining those elements with rows in π1 and columns in π2 is denoted by A(π1 , π2 ), which is of dimension |π1 | × |π2 |. Given ar,c , let Aar,c be the submatrix obtained by deleting row r and column c in the matrix A and let Aar,c be the matrix obtained from A by setting ar,c = 0. Then the determinant det(A) can be expanded as follows: det(A) = ar,c (−1)r+c det(Aar,c ) + det(Aar,c ), (9) where (−1)r+c det(Aar,c ) is called the cofactor of det(A) with respect to ar,c , and det(Aar,c ) as the remainder of det(A) with respect to ar,c .
3. Specifically, let f (x) = xi · g(x) + x¯ i · h(x), where g(x) and h(x) are two cofactors of f (x). If g(x) = h(x), then it immediately follows that g(x) = h(x) = f (x), which means that we do not need to create a BDD node for the variable xi in construction. If such a BDD node is created, it is a superfluous node and should be removed in a post-processing phase to compact BDD. The existence of superfluous nodes also causes the non-uniqueness of BDD. Hence, to have an ultimately irreducible BDD, all superfluous nodes should be removed.