A Theorist's Toolkit 2018 2019 — различия между версиями
Материал из Wiki - Факультет компьютерных наук
(не показано 7 промежуточных версии этого же участника) | |||
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[http://www.mi.ras.ru/~podolskii/files/toolkit/grading.pdf Grading] | [http://www.mi.ras.ru/~podolskii/files/toolkit/grading.pdf Grading] | ||
− | [https://docs.google.com/spreadsheets/d/ | + | [https://docs.google.com/spreadsheets/d/1BoduZt39YA4b5S0EQpohif17hskd4g9R_5iJMV34LQY/edit?usp=sharing Results] |
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+ | [http://www.mi.ras.ru/~podolskii/files/toolkit/col.pdf Colloquium Program] | ||
== Course Materials == | == Course Materials == | ||
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|| 07.03.19 || Chebyshev polynomials, their basic properties. Approximation of OR by a polynomial of degree $\sqrt{n}$. Simultaneous multi-party communication complexity, INDEX and SUM-INDEX, upper and lower bounds. || [http://www.mi.ras.ru/~podolskii/files/toolkit/prob_9.pdf Problem list 9 ] | || 07.03.19 || Chebyshev polynomials, their basic properties. Approximation of OR by a polynomial of degree $\sqrt{n}$. Simultaneous multi-party communication complexity, INDEX and SUM-INDEX, upper and lower bounds. || [http://www.mi.ras.ru/~podolskii/files/toolkit/prob_9.pdf Problem list 9 ] | ||
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+ | || 14.03.19 || PARITY requires exponential size AC^0[3] circuit. || [http://www.mi.ras.ru/~podolskii/files/toolkit/prob_10.pdf Problem list 10 ] | ||
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+ | || 21.03.19 || Generalised discrepancy method. Pattern matrix method. Lower bound on the communication complexity of disjointness. || [http://www.mi.ras.ru/~podolskii/files/toolkit/prob_11.pdf Problem list 11 ] | ||
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Decision trees: [http://homepages.cwi.nl/~rdewolf/publ/qc/dectree.pdf Survey] <br> | Decision trees: [http://homepages.cwi.nl/~rdewolf/publ/qc/dectree.pdf Survey] <br> | ||
Low degree approximation of OR: [http://www.cs.columbia.edu/~rocco/Public/d16.pdf A. Klivans and R. Servedio, Toward Attribute-Efficient Learning of Decision Lists and Parities.] (Section 4.2) <br> | Low degree approximation of OR: [http://www.cs.columbia.edu/~rocco/Public/d16.pdf A. Klivans and R. Servedio, Toward Attribute-Efficient Learning of Decision Lists and Parities.] (Section 4.2) <br> | ||
− | Communication Complexity: [https://books.google.ru/books/about/Communication_Complexity.html?id=yiV6pwAACAAJ&source=kp_book_description&redir_esc=y E. Kushilevitz and N. Nisan: Communication Complexity] (Section 6.5) | + | Communication Complexity: [https://books.google.ru/books/about/Communication_Complexity.html?id=yiV6pwAACAAJ&source=kp_book_description&redir_esc=y E. Kushilevitz and N. Nisan: Communication Complexity] (Section 6.5) <br> |
+ | Boolean Circuits: [http://www.cs.princeton.edu/courses/archive/spr07/cos522/circuitsurvey.ps The Complexity of Finite Functions] <br> | ||
+ | Generalized discrepancy and pattern matrix method: [http://www.csc.kth.se/utbildning/kth/kurser/DD2441/semteo12/lecturenotes/NotesLec12.pdf Lecture notes] |
Текущая версия на 16:52, 5 июня 2020
General Information
Howework deadlines: each week before the lecture.
Course Materials
Date | Summary | Problem list |
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17.01.19 | Анализ Фурье. Базовые определения и формулы. Тестирование линейности. | Problem list 1 |
24.01.19 | Плотности распределений, свертка. Social choice theory. Влияния, дискретные производные функций. Формулы для влияний через коэффициенты Фурье. Оценка влияний монотонных транзитивно-симметричных функций. Общее влияние. Функция голосования максимизирует общее влияние среди монотонных функций. Неравенство Пуанкаре. | Problem list 2 |
31.01.19 | Стабильность, чувствительность к шуму. Оператор шума. Диктаторы самые чувствительные среди сбалансированных. Теорема Эрроу. Оценка сверху на вероятность успеха в системе Кондорсета для произвольной транзитивно-симметричной функции. | Problem list 3 |
31.01.19 | Концентрация на низних степенях. Оценки через влияние и чувствительность к шуму. Индикаторы линейных и афинных подпространств, их спектр. Разрешающие деревья. Подстановка переменных. | Problem list 4 |
07.02.19 | Сужения до афинных подпространств. PAC-модель для равномерного распределения. Сведение изучения функции к нахождению больших коэффициентов Фурье. Изучение функций со сконцентрированным спектром. | Problem list 5 |
14.02.19 | Anti-concentration. Paley-Zygmund inequality. B-reasonability, simple properties. The Bonami Lemma. Anti-concentration of low degree polynomials. FKN Theorem. | Problem list 6 |
21.02.19 | Threshold functions. Chow's parameters. Concentration on degree 1. Polynomial threshold functions. Sparsity, lower and upper bounds. | Problem list 7 |
28.02.19 | Decision trees, sensitivity, block sensitivity, certificate complexity, degree. Polynomial relation between these measures. | Problem list 8 |
07.03.19 | Chebyshev polynomials, their basic properties. Approximation of OR by a polynomial of degree $\sqrt{n}$. Simultaneous multi-party communication complexity, INDEX and SUM-INDEX, upper and lower bounds. | Problem list 9 |
14.03.19 | PARITY requires exponential size AC^0[3] circuit. | Problem list 10 |
21.03.19 | Generalised discrepancy method. Pattern matrix method. Lower bound on the communication complexity of disjointness. | Problem list 11 |
References
Fourier analysis: Ryan O'Donnell Analysis of Boolean Functions
Decision trees: Survey
Low degree approximation of OR: A. Klivans and R. Servedio, Toward Attribute-Efficient Learning of Decision Lists and Parities. (Section 4.2)
Communication Complexity: E. Kushilevitz and N. Nisan: Communication Complexity (Section 6.5)
Boolean Circuits: The Complexity of Finite Functions
Generalized discrepancy and pattern matrix method: Lecture notes