By Gary D. Hachtel

*Logic Synthesis and Verification Algorithms* is a textbook designed for classes on VLSI common sense Synthesis and Verification, layout Automation, CAD and complex point discrete arithmetic. It additionally serves as a easy reference paintings in layout automation for either pros and scholars. *Logic Synthesis and Verification Algorithms* is ready the theoretical underpinnings of VLSI (Very huge Scale built-in Circuits). It combines and integrates smooth advancements in common sense synthesis and formal verification with the extra conventional subject of Switching and Finite Automata idea. The ebook additionally offers history fabric on Boolean algebra and discrete arithmetic.

a special function of this article is the massive selection of solved difficulties.

during the textual content the algorithms lined are the topic of 1 or extra difficulties according to using on hand synthesis programs.

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**Additional info for Logic Synthesis and Verification Algorithms**

**Example text**

Similarly, since for all (here Finally, note that implies that and Similarly, implies that and Thus the “big-O” [161] notation gives a way to express the fact that is an asymptotic upper bound to to within a constant factor, and similarly for the notation. O(1) can be regarded as a conceptual set of asymptotically constant functions, whose value is not specified. Consequently, if all we know is that their exist constants and such that the function F is bounded from above by the constant ( is independent of ) for all Some small examples will help clarify the definition: Example: Note that it is unnecessary to find the smallest constants and that satisfy the definition.

1 Worst Case Asymptotic Upper Bound Complexity Given that an algorithm has to be applied to VLSI (Very Large Scale Integration) CAD applications, it must be efficient and robust for the case of large problem instances. For instance, the control logic on the INTEL P6 chip probably has on the order of logic gates. The design of CAD tools for such large applications requires the development of algorithms that are robust and efficient for large scale applications. This has in turn necessitated the development of some notion of the behavior of an algorithm for asymptotically large problem instances.

Consequently, if all we know is that their exist constants and such that the function F is bounded from above by the constant ( is independent of ) for all Some small examples will help clarify the definition: Example: Note that it is unnecessary to find the smallest constants and that satisfy the definition. 5 suffice. Note also that the the values of the constant coefficients in the equation 36 Chapter 1. 2 Complexity of Algorithms Now suppose that represents the actual operations count for some algorithm applied to some class of problems of size We say that the algorithm, applied to input data of size has worst case asymptotic upper bound complexity if its operations count, satisfies the above definition.