By Prof. Dr. Christoph Meinel, Dr. Thorsten Theobald (auth.)
One of the most difficulties in chip layout is the large variety of attainable mixtures of person chip components, resulting in a combinatorial explosion as chips turn into extra advanced. New key leads to theoretical desktop technological know-how and within the layout of information buildings and effective algorithms could be utilized fruitfully right here. the appliance of ordered binary determination diagrams (OBDDs) has ended in dramatic functionality advancements in lots of computer-aided layout initiatives. This textbook offers an creation to the rules of this interdisciplinary learn region with an emphasis on functions in computer-aided circuit layout and formal verification.
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Extra info for Algorithms and Data Structures in VLSI Design: OBDD — Foundations and Applications
32. There are 2n +1 symmetric functions in n variables. 33. 3 Switching Functions 45 v(f) = (0,1,0,1), v(g) = (0,1,1,1,1), v(h) = (0,0,1,1). (X1,X2,X3) g(X1, X2, X3) h i (X1, ... ,xn ) = X1X2 +X3, = X1X2 + X1X3, = Xi, 1:S i:S n, n:::: 2. <> As the number of symmetric functions is very small in comparison to the total 2n number 2 of all Boolean function in n variables, a randomly chosen function is symmetric only with a very small probability. However, functions which are important for practical applications are not randomly chosen at all.
X n ) = g(Xl,'" ,xn ) = Xik' XiI' XiI + + Xik' 1::; i 1 ::; ::; 1 ::; i 1 ::; ::; ik ::; n, ik ::; n are monotone increasing in each argument. Moreover, in the inessential arguments, f and 9 are also monotone decreasing. 0 Obviously, in all inessential arguments, Boolean functions are both monotone increasing and monotone decreasing. More interesting is the question of monotony in the essential variables. An important contribution to this question is provided by the following representation theorem for monotone functions in the i-th argument which we state without proof.
For example, exactly those vertices of the cube which represent an element in the on-set on(l) are marked. 25. 7 shows a tabular representation and the geometric visualization of the switching function f(XI' X2, xa) = Xl + (X2 . xa). , 42 3. ---+---. 7. Tabular representation and geometric visualization time, space) that can obviously not be provided. However, under certain circumstances, this situation can change dramatically if additional structural properties of the occurring functions are known.
Algorithms and Data Structures in VLSI Design: OBDD — Foundations and Applications by Prof. Dr. Christoph Meinel, Dr. Thorsten Theobald (auth.)