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 turn into extra advanced. New key leads to theoretical desktop technological know-how and within the layout of information constructions and effective algorithms should be utilized fruitfully right here. the applying of ordered binary selection diagrams (OBDDs) has ended in dramatic functionality advancements in lots of computer-aided layout tasks. This textbook presents an advent to the principles of this interdisciplinary learn quarter with an emphasis on functions in computer-aided circuit layout and formal verification.

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**Additional resources for Algorithms and Data Structures in VLSI Design: OBDD — Foundations and Applications**

**Example text**

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. In 1910, the physician P. Ehrenfest vaguely suggested applying Boolean algebra to the design of switching systems (in telephone networks).

If F and G are Boolean formulas, then so are a) (F) + (G), b) (F)· (G), and c) (F). 2 Boolean Formulas and Boolean Functions 31 4. An expression is a Boolean formula if and only if it can be produced by means of finitely many applications of the rules 1, 2, and 3. For the subsequent treatment, we relax this definition slightly. We still call an expression a Boolean formula if it can be derived from a Boolean formula by removing a pair of parentheses, and if this process (by means of the usual parentheses convention) still allows us to recognize the original meaning uniquely.

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. Obviously, Iffin,l coincides with the already defined set Iffin . The immense complexity observed when dealing with switching functions is caused substantially by the very rapid growth of the cardinality of Iffin,m.

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

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