By Jon Kleinberg, Éva Tardos

ISBN-10: 0321295358

ISBN-13: 9780321295354

* Algorithm layout * introduces algorithms by means of the real-world difficulties that encourage them. The ebook teaches scholars a number of layout and research innovations for difficulties that come up in computing functions. The textual content encourages an knowing of the set of rules layout strategy and an appreciation of the function of algorithms within the broader box of computing device science.

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**Sample text**

Therefore, if the fault is testable, there exists a consistent labeling of the neurons in the ATG neural network with values from the set {O,l} that does not violate the functionality of any gate. To obtain a test vector for a given fault, we have to find a minimum energy state of the ATG neural network. The activation values ofthe primary input neurons in the minimum energy state of the ATG network fonn the test vector for the fault. 4 Summary Having discussed the basic fonnulation oftest generation as an energy minimizationproblem, we will develop several new test generation techniques.

Chapter 5 NEURAL MODELING FOR DIGITAL CIRCUITS "Science has little use for models that slavishly obey all our wishes. We want models that talk back to us, models that have a mind oftheir own. We want to get out ofour models more than we have put in. " - T. TofIoli and N. Margolus in Cellular Automata Machines, MIT Press (1987) We can relate the input and output signal states of a logic gate through an energyjunction, defined over a networlc ofneurons, such that the minimumenergy states correspond to the gate's function.

2: Energy surface for EAND. AND VI 0 0 0 0 1 1 1 1 Vi lt1 0 0 0 1 1 0 0 0 0 1 1 0 1 1 1 1 EAND 0 2A+B 0 A 0 A B 0 function ofthe AND gate. 2 shows the value ofthe energy function for all possible states of the network. 3). This neuron has an activation value 1 when both inputs to the gate are 1. 2 gives a mathematical basis for these transformations. 2 Existence of Neural Models We show that an arbitrary logic circuit can be represented by a neural network. The summation of energy functions for the individual gates yields the energy function for the logic circuit.

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