A pseudorandom generator Gn : {0, 1}n → {0, 1}m is hard for a propositional proof system P if (roughly speaking) P can not efficiently prove the statement Gn(x1, . . . , xn) 6= b for any string b ∈ {0, 1}m. We present a function (m ≥ 2nΩ(1)) generator which is hard for Res( log n); here Res(k) is the propositional proof system that extends Resolution by allowing k-DNFs instead of clauses. As a ...

Let $\psi$ be a sentence in the counting monadic second-order logic of matroids and let F finite field. Hlineny's Theorem says that we can test whether F-representable satisfy using an algorithm is fixed-parameter tractable with respect to branch-width. In previous paper proved there similar members any efficiently pigeonhole class. this sequel apply results from first thereby extend classes fu...

Abstract Hliněný’s Theorem shows that any sentence in the monadic second-order logic of matroids can be tested polynomial time, when input is limited to a class $${\mathbb {F}}$$ F -representable with bounded branch-width (where finite field). If each matroid decomposed by subcubic tree such way only amount i...

Recently there has been much interest in data that, in statistical language, may be described as having a large crossed and severely unbalanced random effects structure. Such data sets arise for recommender engines and information retrieval problems. Many large bipartite weighted graphs have this structure too. We would like to assess the stability of algorithms fit to such data. Even for linea...

THE TWO EARLIER ARTICLES IN THIS THREE-PART SERIES focused on the linguistic situation in Belarus and on factors instrumental in shaping Belarusian identity. However, no attempt at understanding Belarus can succeed without examining its economic dynamics and political discourse. The analysis that follows will evaluate Belarus’ accomplishments under the Soviet regime. The point is made that the ...

This article introduces a line of investigation into connections between creature forcings and topological Ramsey spaces. Three examples of pure candidates for creature forcings are shown to contain dense subsets which are actually topological Ramsey spaces. A new variant of the product tree Ramsey theorem is proved in order to obtain the pigeonhole principles for two of these examples.

We examine the proof-theoretic strength of parameterized tree-like resolution—a proof system for the coW[2]complete set of parameterized tautologies. Parameterized resolution and, moreover, a general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider (FOCS’07). In that paper, Dantchev et al. show a complexity gap in parameterized tree-like resolution fo...

Many satisfiability problems called structured SAT problems (like Ramsey, PigeonHole, and so on) may be very shortly defined with Score(FD/B), a boolean constraint programming language design at the Computer Research Center of Dijon (CRID). In addition to the expressiveness, design features of the language (cardinality constraints) are also used to detect some properties (symmetries) of the pro...