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 large variety of attainable combos of person chip parts, resulting in a combinatorial explosion as chips develop into extra advanced. New key leads to theoretical machine technology and within the layout of information buildings and effective algorithms might be utilized fruitfully the following. the appliance of ordered binary selection 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 study zone with an emphasis on functions 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**

0,1) be a Boolean algebra. An n-variable function f : An -t A is called a Boolean function if it is induced by a Boolean formula F. We say that formula F represents the function f. The set of all Boolean functions over B is denoted by Pn(B). 10. Let us consider the set algebra B of the set {I, 2} and the formula F = Xl + Xl = {{I, 2}, U, n, -, 0, {I, 2}} . X2· The tabular representation of the induced Boolean function Fig. 2. f F is shown in 0 Let B = (A; +,', -,0,1) be a Boolean algebra. The set Pn(B) of all n-variable Boolean functions over the algebra B is a subset of the set Fn(A) of all functions from An to A.

The state transitions themselves depend on the current state and on the current input. State transition. As an easy example, let us consider a counter with reset state qo. Whenever the input is 1, the counter periodically traverses the states qo, ql, q2, q3· If the input is 0, then the counter immediately returns to the reset state qo. The behavior of the counter can be precisely described by a transition table or by a state diagram, see Fig. 5. A state diagram is a graph whose nodes are labeled by the names of the states and whose edges characterize the state transitions.

3 be a partial switching function defined on the four inputs (0,0,1),(0,1,0),(1,1,0),(1,1,1) by ](0,0,1) = ](0,1,0) = ](1,1,1) = 1, and ](1,1,0) = 0. Then the don't care set consists of the inputs (0,0,0), (0,1,1), (1,0,0), (1,0,1). $~. We say that the function f is embedded in the set Jan of all completely specified functions. The resulting function l' E lffin is called an extension of f. $~ is 2#dc(f). Keeping in mind that digital circuits only realize completely defined switching functions, one recognizes the significance of the task of constructing best suitable extensions with respect to given optimization criteria.

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

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