Factoring the Growth

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In 1964, R. D. Anderson announced [ l ] that the product of a countably infinite collection of dendra is a Hilbert cube (a dendron being a nondegenerate, uniquely arcwise connected, Peano continuum). He and R. H. Bing conjectured in [4] that a countably infinite product of compact contractible complexes is a Hilbert cube. The purpose of this note is to announce the following theorems which affi...

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Logic programs, when total, realize proofs via a realizability interpretation similar to the Curry Howard isomorphism. The challenge in statically deciding totality lies in checking for termination and for coverage. For Elf logic programs, sophisticated algorithms exist for both problems. However, those solutions only apply to a much smaller subset of logic programs than a programmer is typical...

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Factoring Polynomials

Factoring polynomials over the rational numbers, real numbers, and complex numbers has long been a standard topic of high school algebra. With the advent of computers and the resultant development of error-correcting codes, factoring over finite fields (e.g., Zp, for p a prime number) has become important as well. To understand this discussion, you need to know what polynomials are, and how to ...

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In this lecture we will discuss the problem of integer factorization and primality testing, two problems that have been the focus of a great amount of research over the years. These problems started receiving attention in the mathematics community far before the appearance of computer science, however the emergence of the latter has given them additional importance. Gauss himself wrote in 1801 ...

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ژورنال

عنوان ژورنال: Science

سال: 2012

ISSN: 0036-8075,1095-9203

DOI: 10.1126/science.338.6108.723-a