Ultra low power and energy efficiency requirements are common to most IC designs today. Requirements range from extending battery life to operating on harvested energy, with applications ranging from consumer electronics to medical applications. Design methodologies have evolved over the past decade to cater to low power designs. This panel will discuss the design methodology challenges in the next generation ultra low power and energy efficient IC designs, covering EDA roadmap, low power standards, and design and verification flows.

We investigate the relation between fine-grained and coarse-grained distributed computations of a class of problems related to the generic transitive closure problem (TC for short). We choose an intricate systolic algorithm for the TC problem, by Guibas, Kung and Thompson (GKT algorithm for short), as a starting point due to its particularly close relationship to matrix multiplication. The GKT algorithm reduces the TC problem to three successive parallel matrix multiplications. We extract the main ideas of this algorithm, namely different path decompositions related to min-paths and max-paths computations and devise a two-pass parallel algorithm, such that the second pass is purely a triangular matrix multiplication involving exactly $\frac13$ of the total number of elementary operations (multiplying two single elements of the matrix). This is helpful in coarse-grained parallel computations since matrix multiplication is well parallelizable. A novel approach is used and as a first result a more efficient and simpler two-pass fine-grained algorithm is designed. The second result is a non-trivial transformation of this fine-grained algorithm into a coarse-grained (and more practical) version. The full proof of correctness of the transformation, which is presented in the appendices, is quite complex and is the hardest result of the paper. Our algorithms are specially structured to directly show the correspondence between the main fine-grained and the main coarse-grained operations.

... this paper is to precisely analyse the behaviour of one such extremely simple heuristic which is known to give modest compression in practice. For the heuristic we prove that the expected asymptotic space requirement is, at worst, a(k)n+ b(k)x and that although its dependency on n is inherent, it can be made arbitrarily small. Here k is a parameter and a(k) and b(k) are, respectively, monotonically decreasing and increasing functions. Thus k allows a trade-off between dependency on n and x;for example, pairs (a(k), b(k)) can be (0.1, 3.26), (0.03, 5.57) and (6 10 -4 , 33). We also show that for some applications the dependency of the space requirement on n canbemadesublinear. The heuristic allows constant time access to any element. Our analyses are over two different models for the uniform probability distribution and we derive exact formulae for the expected space used. We prove that the heuristic gives the same asymptotic performance in both models

Complex natural processes may often be expressed in terms of networks of computational components, such as Boolean logic gates or artificial neurons. The interaction of biological molecules and the flow of information controlling the development and behaviour of organisms is particularly amenable to this approach, and these models are well established in the biological community. However, only relatively recently have papers appeared proposing the use of such systems to perform useful, human-defined tasks. Rather than merely using the network analogy as a convenient technique for clarifying our understanding of complex systems, it may now be possible to harness the power of such systems for the purposes of computation. We review several such proposals, focusing on the molecular implementation of fundamental computational elements.

We present an embedding of the complete binary tree with n leaves in the & x & mesh, for any n = 22m where m is a positive integer.