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PVS: A Prototype Verification System
 CADE
, 1992
"... PVS is a prototype system for writing specifications and constructing proofs. Its development has been shaped by our experiences studying or using several other systems and performing a number of rather substantial formal verifications (e.g., [5,6,8]). PVS is fully implemented and freely available. ..."
Abstract

Cited by 655 (16 self)
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automation for an impoverished logic, and others that feature expressive logics but only limited automation. PVS attempts to tread the middle ground between these two classes by providing mechanical assistance to support clear and abstract specifications, and readable yet sound proofs for difficult theorems
The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 506 (2 self)
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from char. o to char. p provided that p> 2g qi. Unfortunately, attempts to extend this method to all p seem to get stuck on difficult questions of wild ramification. Nowadays, the Teichmtiller theory gives a thoroughly analytic but very profound insight into this irreducibility when kC. Our
A combinatorial theorem,
 Journal of the London Mathematical Society
, 1950
"... In this paper we will consider Ramseytype problems for finite graphs, rpartitions and hypergraphs. All these problems ask for the existence of large homogeneous (monochromatic) configurations of a certain kind under the condition that the size of the underlying set is large. As it is quite common ..."
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Cited by 150 (4 self)
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common in Ramsey theory, most of our results are not sharp and almost all of them lead to new problems which seem to be difficult. The problems we treat are only loosely connected. So we will state and explain them section by section.
Social Processes and Proofs of Theorems and Programs
, 1979
"... It is argued that formal verifications of programs, no matter how obtained, will not play the same key role in the development of computer science and software engineering as proofs do in mathematics. Furthermore the absence of continuity, the inevitability of change, and the complexity of specifica ..."
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Cited by 126 (1 self)
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of specification of significantly many real programs make the formal verification process difficult to justify and manage. It is felt that ease of formal verification should not dominate program language design.
Constructivism Is Difficult
"... In a recent issue of this MONTHLY, FredRichman[8] discussed existence proofs. Richman’s conclusion, as I understood it, was that once a mathematician sees the distinction between constructive and nonconstructive mathematics, he or she will choose the former. That conclusion, if extrapolated further ..."
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than Professor Richman intended, suggests that any mathematician can learn constructivism easily if he or she so desires. But in fact constructivism is unusually difficult to learn. Learning most mathematical subjects merely involves adding to one’s knowledge, but learning constructivism involves
Why is optimization difficult?
"... This chapter aims to address some of the fundamental issues that are often encountered in optimization problems, making them difficult to solve. These issues include premature convergence, ruggedness, causality, deceptiveness, neutrality, epistasis, robustness, overfitting, oversimplification, multi ..."
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Cited by 4 (2 self)
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This chapter aims to address some of the fundamental issues that are often encountered in optimization problems, making them difficult to solve. These issues include premature convergence, ruggedness, causality, deceptiveness, neutrality, epistasis, robustness, overfitting, oversimplification
A simple proof and some difficult examples for Hindman’s Theorem
 Notre Dame J. Formal Logic
"... ar ..."
Optimization with Randomized Search Heuristics  The (A)NFL Theorem, Realistic Scenarios, and Difficult Functions
, 2000
"... The No Free Lunch (NFL) theorem due to Wolpert and Macready (1997) has led to controversial discussions on the usefulness of randomized search heuristics, in particular, evolutionary algorithms. Here a short and simple proof of the NFL theorem is given to show its elementary character. Moreover, ..."
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Cited by 35 (1 self)
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The No Free Lunch (NFL) theorem due to Wolpert and Macready (1997) has led to controversial discussions on the usefulness of randomized search heuristics, in particular, evolutionary algorithms. Here a short and simple proof of the NFL theorem is given to show its elementary character. Moreover
Experiments in Theorem Proving and Model Checking for Protocol Verification
, 1996
"... . Communication protocols pose interesting and difficult challenges for verification technologies. The state spaces of interesting protocols are either infinite or too large for finitestate verification techniques like model checking and state exploration. Theorem proving is also not effective sinc ..."
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Cited by 79 (12 self)
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. Communication protocols pose interesting and difficult challenges for verification technologies. The state spaces of interesting protocols are either infinite or too large for finitestate verification techniques like model checking and state exploration. Theorem proving is also not effective
Multipleantenna channel hardening and its implications for rate feedback and scheduling
 IEEE Transactions on Information Theory
, 2004
"... Wireless data traffic is expected to grow over the next few years and the technologies that will provide data services are still being debated. One possibility is to use multiple antennas at basestations and terminals to get very high spectral efficiencies in rich scattering environments. Such multi ..."
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Cited by 159 (2 self)
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approximation of the distribution of the MIMO channel mutual information. Because the exact distribution of the mutual information in a Rayleigh fading environment is difficult to analyze, we prove a central limit theorem for MIMO channels with a large number of antennas. While the growth in average mutual
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