Implementing systems in proof assistants like Coq and proving their correctness in full formal detail has consistently demonstrated promise for making extremely strong guarantees about critical software, ranging from compilers and operating systems to databases and web browsers. Unfortunately, these verications demand such heroic manual proof effort, even for a single system, that the approach has not been widely adopted. We demonstrate a technique to eliminate the manual proof burden for verifying many properties within an entire class of applications, in our case reactive systems, while only expending effort comparable to the manual verication of a single system. A crucial insight of...

**Submitted by:** BmoreDaniel on Jul 21, 2014

In this paper, we present Google, a prototype of a large-scale search engine which makes heavy use of the structure present in hypertext. Google is designed to crawl and index the Web efficiently and produce much more satisfying search results than existing systems. The prototype with a full text and hyperlink database of at least 24 million pages is available at http://google.stanford.edu/ To engineer a search engine is a challenging task. Search engines index tens to hundreds of millions of web pages involving a comparable number of distinct terms. They answer tens of millions of queries every day. Despite the importance of large-scale search engines on the web, very little aca...

**Submitted by:** alixander on Jul 14, 2014

In his celebrated paper [1], A. M. Turing investigated the computability of sequences (functions) by mechanical procedures and showed that the set of sequences can be partitioned into computable and noncomputable sequences. One finds, however, that some computable sequences are very easy to compute whereas other computable sequences seem to have an inherent complexity that makes them difficult to compute. In this paper, we investigate a scheme of classifying sequences according to how hard they are to compute. This scheme puts a rich structure on the computable sequences and a variety of theorems are established. Furthermore, this scheme can be generalized to classify numbers, fu...

**Submitted by:** alixander on Jul 14, 2014

The recent development of various methods of modulation such as PCM and PPM which exchange bandwidth for signal-to-noise ratio has intensified the interest in a general theory of communication. A basis for such a theory is contained in the important papers of Nyquist1 and Hartley2 on this subject. In the present paper we will extend the theory to include a number of new factors, in particular the effect of noise in the channel, and the savings possible due to the statistical structure of the original message and due to the nature of the final destination of the information.

**Submitted by:** alixander on Jul 14, 2014

Quantum Computing is a new and exciting field at the intersection of mathematics, computer science and physics. It concerns a utilization of quantum mechanics to improve the efficiency of computation. Here we present a gentle introduction to some of the ideas in quantum computing. The paper begins by motivating the central ideas of quantum mechanics and quantum computation with simple toy models. From there we move on to a formal presentation of the small fraction of (finite dimensional) quantum mechanics that we will need for basic quantum computation. Central notions of quantum architecture (qubits and quantum gates) are described. The paper ends with a presentation of one of the simple...

**Submitted by:** iamaquantumcomputer on Jul 22, 2014

To what extent should one trust a statement that a program is free of Trojan horses? Perhaps it is more important to trust the people who wrote the software.

**Submitted by:** alixander on Jul 14, 2014

Paper presents tutorial on aspects of floating-point that have a direct impact on designers of computer systems

**Submitted by:** hdd2k on Jul 21, 2014

The blockchain paradigm when coupled with cryptographically-secured transactions has demonstrated its utility through a number of projects, not least Bitcoin. Each such project can be seen as a simple application on a decentralised, but singleton, compute resource. We can call this paradigm a transactional singleton machine with shared-state. Ethereum implements this paradigm in a generalised manner. Furthermore it provides a plurality of such resources, each with a distinct state and operating code but able to interact through a message-passing framework with others. We discuss its design, implementation issues, the opportunities it provides and the future hurdles we envisage.

**Submitted by:** alixander on Jul 14, 2014

We present jump consistent hash, a fast, minimal memory, consistent hash algorithm that can be expressed in about 5 lines of code. In comparison to the algorithm of Karger et al., jump consistent hash requires no storage, is faster, and does a better job of evenly dividing the key space among the buckets and of evenly dividing the workload when the number of buckets changes. Its main limitation is that the buckets must be numbered sequentially, which makes it more suitable for data storage applications than for distributed web caching.

**Submitted by:** alixander on Mar 16, 2015

We give a new proof of Frer's bound for the cost of multiplying n-bit integers in the bit complexity model. Unlike Frer, our method does not require constructing special coecient rings with fast roots of unity. Moreover, we prove the more explicit bound O(n logn Klog n) with K = 8. We show that an optimised variant of Frer's algorithm achieves only K = 16, suggesting that the new algorithm is faster than Frer's by a factor of 2log n. Assuming stan- dard conjectures about the distribution of Mersenne primes, we give yet another algorithm that achieves K = 4.

**Submitted by:** alixander on Jul 15, 2014