Download e-book for iPad: Algorithms and Data Structures in VLSI Design: OBDD — by Prof. Dr. Christoph Meinel, Dr. Thorsten Theobald (auth.)

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

ISBN-10: 3540644865

ISBN-13: 9783540644866

ISBN-10: 3642589405

ISBN-13: 9783642589409

One of the most difficulties in chip layout is the massive variety of attainable combos of person chip components, resulting in a combinatorial explosion as chips turn into extra complicated. New key ends up in theoretical computing device technology and within the layout of knowledge buildings and effective algorithms may 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 tasks. This textbook offers an creation to the rules of this interdisciplinary examine zone with an emphasis on purposes in computer-aided circuit layout and formal verification.

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The following problem is co-NP-complete: Input: An undirected graph with n nodes. Output: "Yes", if there does not exist a cyclic path of length n which traverses each node in the graph exactly once. "No", otherwise. 6 Hashing Hashing. The term hashing denotes data storage and retrieval mechanisms which compute the addresses of the data records from corresponding keys. Formally, a hash function h:X-+A has to be defined which maps the set of keys X to a set of addresses A. A data record with a key x E X is then stored at the address h(x).

X n ) =1 Interval functions Jr,t E lRn , 1 lRn, °:s i=1 k :s n: n if and only if LXi:S k, i=1 :s k :s t :s n: n h,t(X1,'" ,xn ) = 1 if and only if k:S LXi i=1 :s t. 46 3. 34. Some relations among important classes of switching functions: Xl +X2+",+Xn =I~n(XI"" ,X n ), Xl' X2····· X n Mn(XI, •.. k - = I~ n(XI, ... ' , ,Xn ), ,Xn ). o The possibility of representing symmetric functions in terms of interval functions is not exhausted by the examples that have just been stated. In fact, every symmetric function can be represented by a disjunction of interval functions.

X~n, (el ,... ,en)E{O,l}n where xl := Xi, x? := Xi, and a(el, ... ,en) E A. Hence, the function f is defined uniquely by the coefficients a(el, ... ,en). The coefficients a(el' ... ,en) themselves only depend on the function values of f for the inputs (el, ... ,en) E {O,l}n. In the same way, the 2 n coefficients uniquely describing the function g only depend on the function values for the inputs (el' ... , en) E {O, I} n. Hence, if f and g are equivalent, then they are identical. 0 As a consequence of the last proposition and its proof, the number of different n-variable Boolean functions can be determined.

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Algorithms and Data Structures in VLSI Design: OBDD — Foundations and Applications by Prof. Dr. Christoph Meinel, Dr. Thorsten Theobald (auth.)


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