High Performance Computing in Science and Engineering, by Peter Lammers, Kamen N. Beronov, Thomas Zeiser, Franz Durst

By Peter Lammers, Kamen N. Beronov, Thomas Zeiser, Franz Durst (auth.), Arndt Bode, Franz Durst (eds.)

This quantity of excessive functionality Computing in technological know-how and Engineering is totally devoted to the ultimate record of KONWIHR, the Bavarian Competence community for Technical and medical excessive functionality Computing. It comprises the transactions of the ultimate KONWIHR workshop, that used to be held at Technische Universität München, October 14-15, 2004, in addition to extra experiences of KONWIHR learn teams. KONWIHR used to be confirmed by means of the Bavarian country executive with a purpose to aid the vast program of excessive functionality computing in technology and expertise in the course of the nation. KONWIHR is a aiding motion to the set up of the German supercomputer Hitachi SR 8000 within the Leibniz Computing middle of the Bavarian Academy of Sciences. The document covers tasks from simple study in laptop technology to enhance instruments for prime functionality computing in addition to functions from biology, chemistry, electric engineering, geology, arithmetic, physics, computational fluid dynamics, fabrics technology and computing device science.

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Extra info for High Performance Computing in Science and Engineering, Garching 2004: Transactions of the KONWIHR Result Workshop, October 14–15, 2004, Technical University of Munich, Garching, Germany

Example text

The difficulty is that as the number of inputs grows, the truth table increases exponentially in size. 30 Chapter 4 Boolean Functions, Quantum Bits, and Feasibility Thus, representing Boolean functions by their truth tables is alway possible, but is not always feasible. The tables will be large when there are thirty inputs, and when there are over 100, the table would be impossible to write down. The final technical concept we need is having not just a single Boolean function but rather a family [fn ] of Boolean functions, each fn taking n inputs, that are conceptually related.

Take k = log2 (n + 1) . We can hold the total count of 1’s in an x of length n in a k-bit register. So let us mentally draw x going down rather than across and draw to its right an n × k grid, whose rows will represent successive values of this register. , closest to x, but this is not critical. The row to the right of x1 has value 0 (that is, 0k as a Boolean string) if x1 = 0 and value 1 (that is, 10k−1 ) if x1 = 1. As we scan x downward, if xi = 0, then the row of k bits has the same value as the previous one, but if xi = 1, then the register is incremented by 1.

Xn , z1 , . . , zm ) = (x1 , . . , xn , z1 ⊕ y1 , . . , zm ⊕ ym ) instead. The matrix P f is still a permutation matrix, although of even larger dimensions 2n+m × 2n+m . Often left unsaid is what happens if we need h-many “helper bits” to compute the original f . The simple answer is that we can treat them all as extra outputs of the function, allocating extra zj variables as dummy inputs so that the ⊕ trick preserves invertibility. Because h is generally polynomial in n, this does not upset feasibility.

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