Universal p‐ary designs

Universal Optimality for Selected Crossover Designs

Hedayat and Yang earlier proved that balanced uniform designs in the entire class of crossover designs based on t treatments, n subjects, and pD t periods are universally optimal when n· t .t ¡ 1/=2. Surprisingly, in the class of crossover designs with t treatments and p D t periods, a balanced uniform design may not be universally optimal if the number of subjects exceeds t .t ¡ 1/=2. This art...

On Optimum Designs of Universal Switch Blocks

This paper presents a breakthrough decomposition theorem on routing topology and its applications in the designing of universal switch blocks. A switch block of k sides and W terminals on each side is said to be universal (a (k, W )-USB) if it is routable for every set of 2-pin nets with channel density at most W . The optimum USB design problem is to design a (k, W )-USB with the minimum numbe...

New Designs of Universal Reversible Gate Library

We present new algorithms to synthesize exact universal reversible gate library for various types of gates and costs. We use the powerful algebraic software GAP for implementation and examination of our algorithms and the reversible logic synthesis problems have been reduced to group theory problems. It is shown that minimization of arbitrary cost functions of gates and orders of magnitude are ...

Universal upper and lower bounds on energy of spherical designs

Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds are optimal for absolutely monotone potentials in the sense that for the linear programming technique they cannot be improved by using polynomials of the sa...

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