By Guoyong Shi, Sheldon X.-D. Tan, Esteban Tlelo Cuautle (auth.)
This publication presents finished insurance of the hot advances in symbolic research concepts for layout automation of nanometer VLSI structures. The presentation is prepared in elements of basics, easy implementation equipment and functions for VLSI layout. subject matters 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 fresh advances, the Binary choice Diagram (BDD) established ways are studied intensive. The BDD-based hierarchical symbolic research methods, have basically damaged the analog circuit measurement barrier.
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Extra info for Advanced Symbolic Analysis for VLSI Systems: Methods and Applications
1. It frequently occurs in symbolic network analysis that an enormous number of sub-expressions are common, and to represent them in a shared format BDD is probably the best choice. 38 3 Binary Decision Diagram for Symbolic Analysis 2. The common sub-expressions are not identified by directly comparing the expressions themselves, rather they are identified by comparing those objects (determinants or graphs) that generate those expressions. A BDD-based construction is probably the only approach available for taking the advantage of sharing those intermediately generated objects.
Sharing the cofactors in logic operations is another advantage of using BDD as graphical representations of logic functions. It can greatly improve the efficiency of logic operations in a BDD-based logic system. There are many logic operators in Boolean algebra. It turns out that it is unnecessary to define a different routine for each type of logic operators. Brace et al.  proposed that a single triple composed of three logic function, defined by I T E(F, G, H ) = F G + F¯ H , can be used to generate all logic operations in Boolean algebra.
A path of BDD refers to a sequence of connected decision arrows from the BDD root to a terminal. If the path is terminated at the node “1”, it is called a 1-path; otherwise, it is called a 0-path if it is terminated at the node “0”. In BDD a path represents one logic evaluation in that the decisions encountered along the path are the logic values assigned to the variables. Specifically, if the decision variable is xi , then the value of xi = 1 is assigned; otherwise, the decision variable of x¯ i means 28 3 Binary Decision Diagram for Symbolic Analysis x x i g (x) x i f(x) = g(x)h(x) h(x) g(x) x AND i x xi g (x) xi x i i h x (x) i x xi h (x) xi i g (x) h (x) x x i i i x i g (x) h (x) xi xi Fig.