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 parts, resulting in a combinatorial explosion as chips turn into extra advanced. New key leads to theoretical laptop technological know-how and within the layout of knowledge buildings and effective algorithms may be utilized fruitfully right here. the appliance of ordered binary determination diagrams (OBDDs) has resulted in dramatic functionality advancements in lots of computer-aided layout tasks. This textbook offers an advent to the rules of this interdisciplinary examine sector 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**

**Example text**

If A 50p Band BE P then A E P. 8. o 1. A problem A is called NP-hard if all B E NP satisfy: B 50p A. 2. A problem A is called NP-complete, if both A is NP-hard and A E NP. 9. Let A be an NP -complete problem. Then the following holds: 1. If A E P then P = NP. 2. If A (j. P then all NP -complete problems B satisfy B (j. P. Proof. Let A E P, and let B be an arbitrary problem in NP. As in particular A is NP-hard, we have B 50p A. 7 implies B E P. As B was chosen arbitrarily from NP, we have P = NP.

The set of all n-variable switching functions is denoted by Iffin . 15, each n-variable switching function is a Boolean function. If it is clear from the context that the underlying Boolean algebra is the switching algebra, the terms Boolean function and switching function can be used synonymously. If C is a circuit with n inputs signals and m output signals, then the input/output behavior of C can be described in terms of an m-tuple f = (II, ... ,fm) of switching functions. The set of n-variable switching functions with m outputs is denoted by Iffin,m.

In the notation of the previous proof we have a(O,O,O,O) = f(0,0,0,0) = {2}, a(l, 0, 0, 0) = f(5, 0, 0, 0) = {1}. Hence, f( {1}, 0, 0, 0) U = a(el' ez, e3, e4) n {IVI n 0e2 n 0e3 n 0e4 (e1 ,... ,e4)E{O,1}4 = (a(l,O,O,O) n {1}) U (a(O,O,O,O) n {2}) = {1} U {2} = 5, in contradiction to the definition of f. 3 Switching Functions In the following, we discuss the special case of Boolean algebra with two elements, which can be seen as the theoretical foundation of circuit design. The significance of this connection was recognized very early.