Resolution over Linear Equations and Multilinear Proofs

We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, Tseitin graph tautologies and the clique-coloring tautologies in these proof systems. Using the (monotone) interpolation by a communication game technique we establish an exponential-size lower bound on refutations in a certain, considerably strong, fragment of resolution over linear equations, as well as a general polynomial upper bound on (non-monotone) interpolants in this fragment. We then apply these results to extend and improve previous results on multilinear proofs (over fields of characteristic 0), as studied in [RazTzameret06]. Specifically, we show the following: 1. Proofs operating with depth-3 multilinear formulas polynomially simulate a certain, considerably strong, fragment of resolution over linear equations. 2. Proofs operating with depth-3 multilinear formulas admit polynomial-size refutations of the pigeonhole principle and Tseitin graph tautologies. The former improve over a previous result that established small multilinear proofs only for the \emph{functional} pigeonhole principle. The latter are different than previous proofs, and apply to multilinear proofs of Tseitin mod p graph tautologies over any field of characteristic 0. We conclude by connecting resolution over linear equations with extensions of the cutting planes proof system.Comment: 44 page

Sum of squares lower bounds for refuting any CSP

Let $P:\{0,1\}^k \to \{0,1\}$ be a nontrivial $k$-ary predicate. Consider a random instance of the constraint satisfaction problem $\mathrm{CSP}(P)$ on $n$ variables with $\Delta n$ constraints, each being $P$ applied to $k$ randomly chosen literals. Provided the constraint density satisfies $\Delta \gg 1$, such an instance is unsatisfiable with high probability. The \emph{refutation} problem is to efficiently find a proof of unsatisfiability. We show that whenever the predicate $P$ supports a $t$-\emph{wise uniform} probability distribution on its satisfying assignments, the sum of squares (SOS) algorithm of degree $d = \Theta(\frac{n}{\Delta^{2/(t-1)} \log \Delta})$ (which runs in time $n^{O(d)}$) \emph{cannot} refute a random instance of $\mathrm{CSP}(P)$. In particular, the polynomial-time SOS algorithm requires $\widetilde{\Omega}(n^{(t+1)/2})$ constraints to refute random instances of CSP$(P)$ when $P$ supports a $t$-wise uniform distribution on its satisfying assignments. Together with recent work of Lee et al. [LRS15], our result also implies that \emph{any} polynomial-size semidefinite programming relaxation for refutation requires at least $\widetilde{\Omega}(n^{(t+1)/2})$ constraints. Our results (which also extend with no change to CSPs over larger alphabets) subsume all previously known lower bounds for semialgebraic refutation of random CSPs. For every constraint predicate~$P$, they give a three-way hardness tradeoff between the density of constraints, the SOS degree (hence running time), and the strength of the refutation. By recent algorithmic results of Allen et al. [AOW15] and Raghavendra et al. [RRS16], this full three-way tradeoff is \emph{tight}, up to lower-order factors.Comment: 39 pages, 1 figur

Проблемы теоретической интерпретации централизма/децентрализма в федерализме

The article is devoted to the analysis of displacement of a vector of theoretical and empirical judgment of new tendencies in federalism functioning. Authors consider possible ways of development of its potential, initiate new approaches to its reflection and the analysis through a prism of centralism and decentralism in federal relations.Статья посвящена анализу смещения вектора теоретического и эмпирического осмысления новых тенденций в функционировании федерализма. Авторы рассматривают возможные пути развития его потенциала, инициируют новые подходы к его рефлексии и анализу через призму централизма и децентрализма в федеративных отношениях

Централизм и децентрализм в федеративных отношениях: проблемы соотношения принципов

The article analyses the priorities of the principles of centralism and decentralism in the structure of federal relations. The authors consider the problem of regions political subjectivity and centralism model of federal relations, as the reflection characteristics of the present stage of development of Russian statehood.Статья посвящена анализу приоритетов принципов централизма и децентрализма в структуре федеративных отношений. Авторы рассматривают проблему политической субъектности регионов и централистской модели федеративных отношений как отражения особенностей современного этапа развития российской государственности

СРАВНЕНИЕ КЛЮЧЕВЫХ ПРЕДЛОЖЕНИЙ ПО СТИМУЛИРОВАНИЮ ЭКОНОМИКИ ДЛЯ ДОСТИЖЕНИЯ ТЕМПОВ РОСТА ВВП РОССИИ ВЫШЕ СРЕДНЕМИРОВЫХ

At the Presidential meeting on economic issues held May 30, 2017, two programs of socio-economic development of Russia were presented. The program of the Center for Strategic Research (CSR) was developed in line with the traditional approach to the Russian economic management implemented over the past 17 years. The mid-term program of the Russian socio-economic development until 2025 under the name “The Growth Strategy” developed under the RF Presidential order No. Pr-1347 of July 14, 2016, at the initiative of the Stolypin club reflects a new look at the Russian economic policy that takes into account the experience of “economic miracle” countries and replicates successful experience of individual industries and regions of Russia that implies more active involvement of the available mechanisms for boosting the economic growth. At present, the above programs are subject to active debates and the question as to which approach will be adopted remains open. The paper presents a comparison table of key provisions of the two programs. The CSR program developed under the leadership of A. L. Kudrin was not presented for a broad discussion, so its analysis was carried out based on public statements made by A. L. Kudrin as well as individual presentation materials (presentation by A. L. Kudrin at the Gaidar Forum in 2017, at the April HSE conference in 2017 and at the Presidential meeting on May 30, 2017). In his directive towards the implementation of the President’s Message to the Federal Assembly No. 2346, paragraph 1 b) of December 5, 2016, the President set the task “to reach the Russian Federation economy growth rates exceeding the world economic growth rates not later than by 2019-2020” .To start the implementation of the economic policy as early as in 2018, a decision on which of the programs will be implemented must be made urgently.На совещании у Президента по экономическим вопросам 30 мая 2017 г. было представлено две программы социально-экономического развития России. Программа Центра стратегических разработок (ЦСР) разработана в русле традиционного подхода к управлению экономикой России, реализуемого в течение последних 17 лет. Среднесрочная программа социально-экономического развития России до 2025 г. «Стратегия Роста», разработанная по поручению Президента от 14.07.2016 № Пр-1347, по инициативе Столыпинского клуба, отражает новый взгляд на экономическую политику России, заключающийся в реализации опыта стран «экономического чуда» и тиражировании успешного опыта отдельных отраслей и регионов России, что подразумевает более активное задействование механизмов стимулирования экономического роста, доступных государству. В настоящее время идет активное обсуждение указанных программ, и вопрос «Какой подход будет реализован?» остается открытым. В статье представлена таблица - сравнение ключевых тезисов двух программ. Программа ЦСР, разработанная под руководством А. Л. Кудрина, на широкое обсуждение не представлена, поэтому ее анализ проводился на основе публичных заявлений А. Л. Кудрина, а также отдельных презентационных материалах (выступление А. Л. Кудрина на Гайдаровском форуме 2017 г., на Апрельской конференции НИУ ВШЭ 2017 г. и на совещании у Президента 30.05.2017). В поручении по реализации Послания Президента Федеральному Собранию от 05.12.2016 № Пр-2346, п. 1б) Президентом была поставлена задача «достижения не позднее 2019-2020 гг. темпов роста экономики Российской Федерации, превышающих темпы роста мировой экономики». Чтобы приступить к реализации экономической политики уже в 2018 г., решение о том, какая из программ будет реализована, необходимо уже сейчас

Противоречия современной версии российского федерализма: нестабильность системы

In the article there considered contradictions of the modern version of the Russian federalism, as a political and politological problem. The authors made an attempt to present the problem of federalism at conceptually-analytical level as a certain ritual meaning of the certain form of a state system thereby its values substance becomes an object of analysis. Besides applied function of federalism it's necessary to see the process of its perception and acceptance by national multinational consciousness through a prism of stability of political process, political practice, actions of the state institutes of power, persons and leaders of the center and regions.В статье рассматриваются противоречия современной версии российского федерализма как политической и политологической проблемы. Делается попытка на концептуально-аналитическом уровне представить проблему федерализма как некий ритуальный смысл определенной формы государственного устройства, тем самым на уровень анализа возводится его ценностная субстанция. Помимо прикладного предназначения федерализма достойно видеть процесс его восприятия и принятия народным многонациональным сознанием через призму стабильности политического процесса, политическую практику, действия государственных институтов власти, персон и лидеров центра и регионов

Стратегический анализ и прогнозирование политических процессов

The article is devoted to the methodology of evaluation and prognosis of political processes and actions in the context of situational and system analysis. The authors propose the model of determination of role political action, which includes several levels: 1) institutional (economical, political and social environment); 2) organizational (structure, non-formal relations, informational processes in institutesand organizations); 3) administrative (administrative environment of organization); 4) groups - parameters and features of contact groups; 5) personal (subjective meanings, values and motives of political actions).Статья посвящена методологии оценки и прогнозирования политических процессов и действий, представленной понятиями ситуационного и системного анализа. Предлагается модель детерминации ролевого политического действия, которая включает несколько уровней: 1) институциональный (экономическая, политическая и социальная среда); 2) организационный (структура, неформальные отношения, информационные процессы в институтах и организациях); 3) административный (административная среда организации); 4) групповой - параметры и свойства контактных групп; и 5) личностный (субъективные значения, ценности и мотивы политических действий)

Width and size of regular resolution proofs

This paper discusses the topic of the minimum width of a regular resolution refutation of a set of clauses. The main result shows that there are examples having small regular resolution refutations, for which any regular refutation must contain a large clause. This forms a contrast with corresponding results for general resolution refutations.Comment: The article was reformatted using the style file for Logical Methods in Computer Scienc

Parameterized bounded-depth Frege is not optimal

A general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider [9]. There the authors concentrate on tree-like Parameterized Resolution-a parameterized version of classical Resolution-and their gap complexity theorem implies lower bounds for that system. The main result of the present paper significantly improves upon this by showing optimal lower bounds for a parameterized version of bounded-depth Frege. More precisely, we prove that the pigeonhole principle requires proofs of size n in parameterized bounded-depth Frege, and, as a special case, in dag-like Parameterized Resolution. This answers an open question posed in [9]. In the opposite direction, we interpret a well-known technique for FPT algorithms as a DPLL procedure for Parameterized Resolution. Its generalization leads to a proof search algorithm for Parameterized Resolution that in particular shows that tree-like Parameterized Resolution allows short refutations of all parameterized contradictions given as bounded-width CNF's