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4,467
The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
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Cited by 682 (76 self)
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.html The articles [4], [6], [1], [2], [5], and [3] provide the notation and terminology for this paper. A natural number is an element of N. For simplicity, we use the following convention: x is a real number, k, l, m, n are natural numbers, h, i, j are natural numbers, and X is a subset of R
The Reflection Theorem
 Journal of Formalized Mathematics
, 1990
"... this paper (and in another Mizar articles) we work in TarskiGrothendieck (TG) theory (see [17]) which ensures the existence of sets that have properties like universal class (i.e. this theory is stronger than MK). The sets are introduced in [15] and some concepts of MK are modeled. The concepts are ..."
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Cited by 251 (51 self)
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this paper (and in another Mizar articles) we work in TarskiGrothendieck (TG) theory (see [17]) which ensures the existence of sets that have properties like universal class (i.e. this theory is stronger than MK). The sets are introduced in [15] and some concepts of MK are modeled. The concepts are: the class On of all ordinal numbers belonging to the universe, subclasses, transfinite sequences of nonempty elements of universe, etc. The reflection theorem states that if A ¸ is an increasing and continuous transfinite sequence of nonempty sets and class A =
A user guide to HYTECH
, 1995
"... HyTech is a tool for the automated analysis of embedded systems. This document, designed for the rsttime user of HyTech, guides the reader through the underlying system model, and through the input language for describing and analyzing systems. The guide gives installation instructions, several exa ..."
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Cited by 159 (4 self)
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HyTech is a tool for the automated analysis of embedded systems. This document, designed for the rsttime user of HyTech, guides the reader through the underlying system model, and through the input language for describing and analyzing systems. The guide gives installation instructions, several examples of usage, some hints for gaining maximal computational e ciency from the tool, and the complete grammar for the input language. This guide describes version 1.04 of HyTech. The latest update occurred in October 1996 1. HyTech is available through the WorldWide Web at
Implementing Gentry’s fullyhomomorphic encryption scheme
 of Lecture Notes in Computer Science
"... We describe a working implementation of a variant of Gentry’s fully homomorphic encryption scheme (STOC 2009), similar to the variant used in an earlier implementation effort by Smart and Vercauteren (PKC 2010). Smart and Vercauteren implemented the underlying “somewhat homomorphic ” scheme, but wer ..."
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Cited by 130 (3 self)
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We describe a working implementation of a variant of Gentry’s fully homomorphic encryption scheme (STOC 2009), similar to the variant used in an earlier implementation effort by Smart and Vercauteren (PKC 2010). Smart and Vercauteren implemented the underlying “somewhat homomorphic ” scheme, but were not able to implement the bootstrapping functionality that is needed to get the complete scheme to work. We show a number of optimizations that allow us to implement all aspects of the scheme, including the bootstrapping functionality. Our main optimization is a keygeneration method for the underlying somewhat homomorphic encryption, that does not require full polynomial inversion. This reduces the asymptotic complexity from Õ(n2.5) to Õ(n1.5) when working with dimensionn lattices (and practically reducing the time from many hours/days to a few seconds/minutes). Other optimizations include a batching technique for encryption, a careful analysis of the degree of the decryption polynomial, and some space/time tradeoffs for the fullyhomomorphic scheme. We tested our implementation with lattices of several dimensions, corresponding to several security levels. From a “toy ” setting in dimension 512, to “small, ” “medium, ” and “large” settings in dimensions 2048, 8192, and 32768, respectively. The publickey size ranges in size from 70 Megabytes for the “small ” setting to 2.3 Gigabytes for the “large ” setting. The time to run one bootstrapping operation (on a 1CPU 64bit machine with large memory) ranges from 30 seconds for the “small ” setting to 30 minutes for the “large ” setting. 1
Combinatorial Commutative Algebra
, 2004
"... The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geo ..."
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Cited by 125 (5 self)
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The last decade has seen a number of exciting developments at the intersection of commutative algebra with combinatorics. New methods have evolved out of an influx of ideas from such diverse areas as polyhedral geometry, theoretical physics, representation theory, homological algebra, symplectic geometry, graph theory, integer programming, symbolic computation, and statistics. The purpose of this volume is to provide a selfcontained introduction to some of the resulting combinatorial techniques for dealing with polynomial rings, semigroup rings, and determinantal rings. Our exposition mainly concerns combinatorially defined ideals and their quotients, with a focus on numerical invariants and resolutions, especially under gradings more refined than the standard integer grading. This project started at the COCOA summer school in Torino, Italy, in June 1999. The eight lectures on monomial ideals given there by Bernd Sturmfels were later written up by Ezra Miller and David Perkinson and published in [MP01]. We felt it would be nice to add more material and
Introduction to the CoNLL2004 Shared Task: Semantic Role Labeling
, 2004
"... In this paper we describe the CoNLL2004 shared task: semantic role labeling. We introduce ..."
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Cited by 124 (2 self)
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In this paper we describe the CoNLL2004 shared task: semantic role labeling. We introduce
Directed sets, nets, ideals, filters, and maps
 Journal of Formalized Mathematics
, 1996
"... Summary. Notation and facts necessary to start with the formalization of continuous lattices according to [8] are introduced. The article contains among other things, the definition of directed and filtered subsets of a poset (see 1.1 in [8, p. 2]), the definition of nets on the poset (see 1.2 in [8 ..."
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Cited by 117 (31 self)
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Summary. Notation and facts necessary to start with the formalization of continuous lattices according to [8] are introduced. The article contains among other things, the definition of directed and filtered subsets of a poset (see 1.1 in [8, p. 2]), the definition of nets on the poset (see 1.2 in [8, p. 2]), the definition of ideals and filters and the definition of maps preserving arbitrary and directed sups and arbitrary and filtered infs (1.9 also in [8, p. 4]). The concepts of semilattices, supsemiletices and poset lattices (1.8 in [8, p. 4]) are also introduced. A number of facts concerning the above notion and including remarks 1.4, 1.5, and 1.10 from [8, pp. 3–5] is presented.
JRes: A Resource Accounting Interface for Java
, 1998
"... With the spread of the Internet the computing model on server systems is undergoing several important changes. Recent research ideas concerning dynamic operating system extensibility are finding their way into the commercial domain, resulting in designs of extensible databases and Web servers. In ad ..."
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Cited by 105 (4 self)
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With the spread of the Internet the computing model on server systems is undergoing several important changes. Recent research ideas concerning dynamic operating system extensibility are finding their way into the commercial domain, resulting in designs of extensible databases and Web servers. In addition, both ordinary users and service providers must deal with untrusted downloadable executable code of unknown origin and intentions. Across the board, Java has emerged as the language of choice for Internetoriented software. We argue that, in order to realize its full potential in applications dealing with untrusted code, Java needs a flexible resource accounting interface. The design and prototype implementation of such an interface  JRes  is presented in this paper. The interface allows to account for heap memory, CPU time, and network resources consumed by individual threads or groups of threads. JRes allows limits to be set on resources available to threads and it can invoke...
Russian Privatization and Corporate Governance: What Went Wrong
 Privatization and Company Restructuring in
, 2000
"... In Russia and elsewhere, proponents of rapid, mass privatization of stateowned enterprises (ourselves among them) hoped that the profit incentives unleashed by privatization would soon revive faltering, centrally planned economies. The revival didn’t happen. We offer here some partial explanations. ..."
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Cited by 104 (0 self)
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In Russia and elsewhere, proponents of rapid, mass privatization of stateowned enterprises (ourselves among them) hoped that the profit incentives unleashed by privatization would soon revive faltering, centrally planned economies. The revival didn’t happen. We offer here some partial explanations. First, rapid mass privatization is likely to lead to massive selfdealing by managers and controlling shareholders unless (implausibly in the initial transition from central planning to markets) a country has a good infrastructure for controlling selfdealing. Russia accelerated the selfdealing process by selling control of its largest enterprises cheaply to crooks, who transferred their skimming talents to the enterprises they acquired, and used their wealth to further corrupt the government and block reforms that might constrain their actions. Second, profit incentives to restructure privatized businesses and create new ones can be swamped by the burden on business imposed by a combination of (among other things) a punitive tax system, official corruption, organized crime, and an unfriendly bureaucracy.
Learning motion patterns of people for compliant robot motion
, 2004
"... Whenever people move through their environments they do not move randomly. Instead, they usually follow specific trajectories or motion patterns corresponding to their intentions. Knowledge about such patterns enables a mobile robot to robustly keep track of persons in its environment and to improve ..."
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Cited by 103 (3 self)
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Whenever people move through their environments they do not move randomly. Instead, they usually follow specific trajectories or motion patterns corresponding to their intentions. Knowledge about such patterns enables a mobile robot to robustly keep track of persons in its environment and to improve its behavior. In this paper we propose a technique for learning collections of trajectories that characterize typical motion patterns of persons. Data recorded with laserrange finders are clustered using the expectation maximization algorithm. Based on the result of the clustering process, we derive a hidden Markov model that is applied to estimate the current and future positions of persons based on sensory input. We also describe how to incorporate the probabilistic belief about the potential trajectories of persons into the path planning process of a mobile robot. We present several experiments carried out in different environments with a mobile robot equipped with a laserrange scanner and a camera system. The results demonstrate that our approach can reliably learn motion patterns of persons, can robustly estimate and predict positions of persons, and can be used to improve the navigation behavior of a mobile robot.
Results 1  10
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4,467