On August 6, 2002,a paper with the title “PRIMES is in P”, by M. Agrawal, N. Kayal, and N. Saxena, appeared on the website of the Indian Institute of Technology at Kanpur, India. In this paper it was shown that the ...
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ISBN:
(数字)9783540259336
ISBN:
(纸本)9783540403449
On August 6, 2002,a paper with the title “PRIMES is in P”, by M. Agrawal, N. Kayal, and N. Saxena, appeared on the website of the Indian Institute of Technology at Kanpur, India. In this paper it was shown that the “primality problem”hasa“deterministic algorithm” that runs in “polynomial time”. Finding out whether a given number n is a prime or not is a problem that was formulated in ancient times, and has caught the interest of mathema- ciansagainandagainfor centuries. Onlyinthe 20thcentury,with theadvent of cryptographic systems that actually used large prime numbers, did it turn out to be of practical importance to be able to distinguish prime numbers and composite numbers of signi?cant size. Readily, algorithms were provided that solved the problem very e?ciently and satisfactorily for all practical purposes, and provably enjoyed a time bound polynomial in the number of digits needed to write down the input number n. The only drawback of these algorithms is that they use “randomization” — that means the computer that carries out the algorithm performs random experiments, and there is a slight chance that the outcome might be wrong, or that the running time might not be polynomial. To ?nd an algorithmthat gets by without rand- ness, solves the problem error-free, and has polynomial running time had been an eminent open problem in complexity theory for decades when the paper by Agrawal, Kayal, and Saxena hit the web.
This book constitutes the proceedings of the 29th International Conference on Case-Based Reasoning, ICCBR 2021, which took place in Salamanca, Spain, during September 13-16, 2021.;The 21 papers presented in this volum...
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ISBN:
(数字)9783030869571
ISBN:
(纸本)9783030869564
This book constitutes the proceedings of the 29th International Conference on Case-Based Reasoning, ICCBR 2021, which took place in Salamanca, Spain, during September 13-16, 2021.;The 21 papers presented in this volume were carefully reviewed and selected from 85 submissions. They deal with AI and related research focusing on comparison and integration of CBR with other AI methods such as deep learning architectures, reinforcement learning, lifelong learning, and eXplainable AI (XAI).
This book constitutes the refereed proceedings of the 25th International Conference on Concurrency Theory, CONCUR 2014, held in Rome, Italy in September 2014. The 35 revised full papers presented together with 5 invit...
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ISBN:
(数字)9783662445846
ISBN:
(纸本)9783662445839
This book constitutes the refereed proceedings of the 25th International Conference on Concurrency Theory, CONCUR 2014, held in Rome, Italy in September 2014. The 35 revised full papers presented together with 5 invited talks were carefully reviewed and selected from 124 submissions. The focus of the conference is on the following topics: process calculi, model checking and abstraction, synthesis, quantitative models, automata and multithreading, complexity, process calculi and types, categories, graphs and quantum systems, automata and time, and games.
This book constitutes the proceedings of the 6th International Symposium on Algorithmic Game Theory, SAGT 2013, held in Aachen, Germany, in October 2013. The 25 papers presented in this volume were carefully reviewed ...
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ISBN:
(数字)9783642413926
ISBN:
(纸本)9783642413919
This book constitutes the proceedings of the 6th International Symposium on Algorithmic Game Theory, SAGT 2013, held in Aachen, Germany, in October 2013. The 25 papers presented in this volume were carefully reviewed and selected from 65 submissions. They cover various important aspects of algorithmic game theory, such as solution concepts in game theory, efficiency of equilibria and the price of anarchy, computational aspects of equilibria and game theoretical measures, repeated games and convergence of dynamics, evolution and learning in games, coordination and collective action, network games and graph-theoretic aspects of social networks, voting and social choice, as well as algorithmic mechanism design.
This book constitutes the thoroughly refereed conference proceedings of the Third International Conference on Algorithmic Decision Theory, ADT 2013, held in November 2013 in Bruxelles, Belgium. The 33 revised full pap...
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ISBN:
(数字)9783642415753
ISBN:
(纸本)9783642415746
This book constitutes the thoroughly refereed conference proceedings of the Third International Conference on Algorithmic Decision Theory, ADT 2013, held in November 2013 in Bruxelles, Belgium. The 33 revised full papers presented were carefully selected from more than 70 submissions, covering preferences in reasoning and decision making, uncertainty and robustness in decision making, multi-criteria decision analysis and optimization, collective decision making, learning and knowledge extraction for decision support.
This book constitutes the refereed proceedings of the 5th International Castle Meeting on Coding Theory and Applications, ICMCTA 2017, held in Vihula, Estonia, in August 2017.
ISBN:
(数字)9783319662787
ISBN:
(纸本)9783319662770
This book constitutes the refereed proceedings of the 5th International Castle Meeting on Coding Theory and Applications, ICMCTA 2017, held in Vihula, Estonia, in August 2017.
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