By Prof. Dr. Christoph Meinel, Dr. Thorsten Theobald (auth.)

One of the most difficulties in chip layout is the massive variety of attainable mixtures of person chip components, resulting in a combinatorial explosion as chips turn into extra advanced. New key ends up in theoretical machine technology and within the layout of knowledge constructions and effective algorithms might be utilized fruitfully right here. the applying of ordered binary selection diagrams (OBDDs) has ended in dramatic functionality advancements in lots of computer-aided layout tasks. This textbook presents an creation to the principles of this interdisciplinary learn region with an emphasis on purposes in computer-aided circuit layout and formal verification.

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**Extra resources for Algorithms and Data Structures in VLSI Design: OBDD — Foundations and Applications**

**Example text**

This can be explained as follows. If there were real weights WI, Wz and a threshold value k satisfying 1 = T W1 ,W2;k, then the following inequalities would hold: o. WI + 1 . Wz 1 . WI + 0 . Wz 1 . WI + 1 . Wz 2: k (since 1(0,1) = 1), 2: k (since 1(1,0) = 1), < k (since 1(1,1) = 0). 48 3. Boolean Functions The first two inequalities can be combined to Wj +W2 ::::: 2k, which contradicts the third equation. Consequently, the function f cannot be represented in terms of a weighted threshold function.

12. , -, 0,1) be a Boolean algebra. , -,Q,l) of all n-variable functions over B. D It is an interesting fact that the relationship between Boolean formulas and Boolean functions is not one-to-one: many different formulas represent the same Boolean functions. An important and central task in many applications of Boolean algebra is to find "good" formulas - according to problem-specific quality criteria - for representing certain concrete Boolean functions under investigation. 13. The Boolean formulas (Xl + X2)· (X3 + X2 .

An (w, w')-polynomial is an w' -product of w-monomials. The length of an (w, w') -polynomial is the sum of lengths of its monomials. (', +)-polynomials are called disjunctive normal forms (DNF). )-polynomials are called conjunctive normal forms (CNF). (', EB)-polynomials are called parity normal forms (PNF). We assume that there are no trivial redundancies like multiple occurrences of literals or terms, and that the order of terms is of not particular importance. 5. DNF representation: d = Xl Xo YI + Xl Xo YI Yo, CNF representation: c = Xl YI + Xo + YI + Yo), PNF representation: p (Xl = Xl Xo YI EB Xl Xo YI Yo· Usually, one is interested in rather short representations.