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 develop into extra advanced. New key leads to theoretical computing device technological know-how and within the layout of knowledge constructions and effective algorithms should be utilized fruitfully right here. the appliance of ordered binary choice diagrams (OBDDs) has ended in dramatic functionality advancements in lots of computer-aided layout initiatives. This textbook presents an advent to the rules of this interdisciplinary learn region with an emphasis on purposes in computer-aided circuit layout and formal verification.

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Consequently, representations of switching functions in terms of truth tables are far from being compact. 2 Two-Level Normal Forms Switching functions can be represented in terms of expressions that combine literals by means of suitable operators. Here, normal forms based on levelized expressions are of particular importance. The number of levels denotes the number of iterated applications of operators, where within a level, only one and the same operator may be employed. One-level normal forms merely use a single operator.

In case an = a the theorem immediately follows from the equation f(al,'" ,an) = g(al,'" ,an-d· In case an = 1 it follows from the equation f(al,'" ,an) = h(al,'" ,an-I). D Xl, ... A subfunction originates from fixing one or several input variables. For this reason, each subfunction of a function f E l$n can be specified by a vector c E {a, 1, id} n. If the i-th component of c is the constant a or 1, the i-th input variable Xi in f is set to a or 1, respectively; if Ci has the value id, then the variable Xi remains unfixed.

6. Let A and B two problems. A is called polynomial time reducible to B, if, under the assumption that arbitrary instances of B can be solved in constant time, a polynomial time algorithm for A exists. We write A 50p B. 7. 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.

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