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.)

One of the most difficulties in chip layout is the large variety of attainable mixtures of person chip parts, resulting in a combinatorial explosion as chips turn into extra complicated. New key ends up in theoretical laptop technological know-how and within the layout of knowledge buildings and effective algorithms could be utilized fruitfully right here. the applying of ordered binary choice diagrams (OBDDs) has resulted in dramatic functionality advancements in lots of computer-aided layout tasks. This textbook offers 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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Here, x? and x} are defined by x} = Xi and x? = Xi. The number l of occurring literals is called the length of m. 3. -monomials: x? X2 xg, x? X4, + -monomials: Xl x2 X5 x7 xs, x? + x2 + xg + x? + X4, EEl -monomials: x? EEl X2 EEl xg EEl x? EEl X4, Xl + X2 + x5 + X7 + xs, Xl EEl X2 EEl X5 EEl X7 EEl xs, <> 54 4. Classical Representations . -monomials m = X~:l ... X~lil are simply called monomials. As already mentioned, the operator· is often omitted. The empty monomial is defined to be the tautology function 1.

One "guesses" a satisfying assignment, and then applies substitutions in order to verify that all clauses are satisfied for this input (which is obviously possible in polynomial time).

Parity function PARn E lRn : n PARn(Xl, ... ,x n ) = ffii=1Xi = (Lx;) (mod 2), i=1 Majority function M n E lRn: n M n (X1, ... ,xn ) = 1 if and only if Threshold functions Tr E lRn, °:s LXi::::~' i=1 k :s n: n Tr(X1, . , x n ) = 1 if and only if LXi:::: k, Inverse threshold functions T Sk E T Sk (X1, ... , 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, •..

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