By Sabih H. Gerez
Modern microprocessors resembling Intel's Pentium chip in general comprise thousands of transitors. identified generically as Very Large-Scale built-in (VLSI) platforms, the chips have a scale and complexity that has necessitated the advance of CAD instruments to automate their layout. This booklet makes a speciality of the algorithms that are the development blocks of the layout automation software program which generates the format of VLSI circuits. one of many first books at the topic, this advisor covers all levels of design.
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Extra info for Algorithms for VLSI Design Automation
An introduction to a technique that can be used for this purpose is presented in Chapter I 1. g. to check that all possible conditions are covered in the case ofa conditional computation. Yet another issue related to formal verification is correctness by construction. one can see the design process as the subsequent application of small transformations on an initial design. Each transformation adds some detail to an intermediate design until the final design has been obtained. If one can prove that all transformations that one intends to use preserve the behavior of the system, one can conclude that final design is "correct by construction" (assuming that the initial specifications were correct).
The case for Dijkstra's shortest-path algorithm. As it will be shown later, its time complexity is a polynomial function of n (the numberof vertices) and lEl in spite of the fact that the number of paths may grow exponentially with n and lE l. This is due to the fact that many nonoptimal paths are directly eliminated while the algorithm proceeds. 14. 4). In its main loop, the vertices of the set V are transferred one by one to a set I. e. it will not change in the next iterations). Therefore, if the vertex to be transferred corresponds to ur, the algorithm can stop.
Tractable and lntractable Problems 45 involves the computation of the cost function, given a feasible solution. For most problems it can be done in polynomial time. 3 Complexity Classes For the purpose of reasoning about the degree of difficulty of decision problems, it is useful to group problems with the same degree in one complexity class. The class of decision problems for which an algorithm is known that operates in polynomial time is called P (which is an abbreviation of "polynomial"). Before introducing another class called NP, it is necessary to give an informal definition of a nondeterministic computer.