Boolean function

Abstract: This article gives a survey of recent results that connect three areas in com- puter science and mathematics: (1) (Hardness of) computing approximate solutions to NP-complete problems. (2) Fourier analysis of boolean functions on boolean hypercube. (3) Certain problems in geometry, especially related to isoperimetry and embeddings between metric spaces.

Abstract: Reversible logic serves as a basis for emerging technologies like quantum computing and additionally has applications in low-power design. In particular, since conventional technologies like CMOS are going to reach their limits in the near future, reversible logic has been established as a promising alternative. Thus, in the last years this area started to become intensely studied by researchers. In particular, how to efficiently synthesize complex reversible circuits is an important question. So far, only synthesis approaches are available that rely on Boolean function representations, like e.g., truth tables or decision diagrams.

Abstract: 1. Relationships between monotone and non-monotone network complexity 2. On read-once Boolean functions 3. Boolean function complexity: a lattice-theoretic perspective 4. Monotone complexity 5. On submodular complexity measures 6. Why is Boolean complexity so difficult? 7. The multiplicative complexity of Boolean quadratic forms 8. Some problems involving Razborov-Smolensky polynomials 9. Symmetry functions in AC0 10. Boolean complexity and probabilistic constructions 11. Networks computing Boolean functions for multiple input values 12. Optimal carry save networks.

Abstract: Reviewed by Michaele E. Duncan, University of Southern Mississippi Technical Editor: Marcin Paprzycki Dept. of Computer Science and Statistics Univ. of Southern Mississippi Southern Station 1506 Hattiesburg, MS 39406-1506 m.paprzycki@usm.edu In Search of Clusters began as an attempt to collect a set of terms and definitions that would define and describe various aspects of computer clusters; Gregory Pfister accomplishes this goal and more. His obvious sense of humor and generous use of metaphors make a potentially boring subject incredibly interesting—even fun. In Search of Clusters contains valuable information for the novice and expert alike. The reader need only have a limited understanding of computers and the associated terminology to benefit from this book. However, while easy to understand, there is a wealth of technical “hard stuff” to keep the computer gurus interested. It is a must read for anyone considering assembling a cluster. Pfister divides the book into four basic parts. First, he covers the concepts of clusters, explaining how and why they can solve complex problems. He includes many detailed examples of clusters that help the reader grasp the concepts, as well as definitions and comparisons of clusters and associated terminology. The reader learns to distinguish between parallel and distributed systems. Secondly, Pfister discusses the hardware possibilities involved in clustering machines. He begins with the four basic categories of hardware structures and how to establish communication. Following this, discussions on cluster alteration techniques, symmetric multiprocessors, NUMA, UMA, and Norma show the multiple hardware avenues available, along with the advantages and disadvantages of each. Thirdly, Pfister addresses the software aspects of clusters. Chapters on workloads, basic programming models and issues, commercial programming models, and single-system image help explain the often overlooked complexities of the software side of clustering. Finally, Pfister ties everything together in a section on systems. His effective style of presentation, along with over 100 figures and 20 tables, make In Search of Clusters a very interesting and informative book. While this is not applicable as a text book, it would be extremely beneficial as required reading in any computer-related course on networking or parallel processing at the undergraduate or graduate level. Book Reviews