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All reports by Author Dmitry Itsykson:

TR20-184 | 10th December 2020
Dmitry Itsykson, Artur Riazanov

Proof complexity of natural formulas via communication arguments

A canonical communication problem ${\rm Search}(\phi)$ is defined for every unsatisfiable CNF $\phi$: an assignment to the variables of $\phi$ is distributed among the communicating parties, they are to find a clause of $\phi$ falsified by this assignment. Lower bounds on the randomized $k$-party communication complexity of ${\rm Search}(\phi)$ in ... more >>>

TR20-073 | 5th May 2020
Sam Buss, Dmitry Itsykson, Alexander Knop, Artur Riazanov, Dmitry Sokolov

Lower Bounds on OBDD Proofs with Several Orders

This paper is motivated by seeking lower bounds on OBDD($\land$, weakening, reordering) refutations, namely OBDD refutations that allow weakening and arbitrary reorderings. We first work with 1-NBP($\land$) refutations based on read-once nondeterministic branching programs. These generalize OBDD($\land$, reordering) refutations. There are polynomial size 1-NBP($\land$) refutations of the pigeonhole principle, hence ... more >>>

TR20-067 | 30th April 2020
Dmitry Itsykson, Alexander Okhotin, Vsevolod Oparin

Computational and proof complexity of partial string avoidability

The partial string avoidability problem is stated as follows: given a finite set of strings with possible ``holes'' (wildcard symbols), determine whether there exists a two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol. The problem is known to be NP-hard and in ... more >>>

TR19-178 | 5th December 2019
Dmitry Itsykson, Artur Riazanov, Danil Sagunov, Petr Smirnov

Almost Tight Lower Bounds on Regular Resolution Refutations of Tseitin Formulas for All Constant-Degree Graphs

We show that the size of any regular resolution refutation of Tseitin formula $T(G,c)$ based on a graph $G$ is at least $2^{\Omega(tw(G)/\log n)}$, where $n$ is the number of vertices in $G$ and $tw(G)$ is the treewidth of $G$. For constant degree graphs there is known upper bound $2^{O(tw(G))}$ ... more >>>

TR19-069 | 6th May 2019
Nicola Galesi, Dmitry Itsykson, Artur Riazanov, Anastasia Sofronova

Bounded-depth Frege complexity of Tseitin formulas for all graphs

Revisions: 1

We prove that there is a constant $K$ such that \emph{Tseitin} formulas for an undirected graph $G$ requires proofs of
size $2^{\mathrm{tw}(G)^{\Omega(1/d)}}$ in depth-$d$ Frege systems for $d<\frac{K \log n}{\log \log n}$, where $\tw(G)$ is the treewidth of $G$. This extends H{\aa}stad recent lower bound for the grid graph ... more >>>

TR19-020 | 4th February 2019
Ludmila Glinskih, Dmitry Itsykson

On Tseitin formulas, read-once branching programs and treewidth

Revisions: 1

We show that any nondeterministic read-once branching program that computes a satisfiable Tseitin formula based on an $n\times n$ grid graph has size at least $2^{\Omega(n)}$. Then using the Excluded Grid Theorem by Robertson and Seymour we show that for arbitrary graph $G(V,E)$ any nondeterministic read-once branching program that computes ... more >>>

TR19-001 | 5th January 2019
Dmitry Itsykson, Alexander Knop, Andrei Romashchenko, Dmitry Sokolov

On OBDD-based algorithms and proof systems that dynamically change order of variables

In 2004 Atserias, Kolaitis and Vardi proposed OBDD-based propositional proof systems that prove unsatisfiability of a CNF formula by deduction of identically false OBDD from OBDDs representing clauses of the initial formula. All OBDDs in such proofs have the same order of variables. We initiate the study of OBDD based ... more >>>

TR18-041 | 26th February 2018
Sam Buss, Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

Reordering Rule Makes OBDD Proof Systems Stronger

Atserias, Kolaitis, and Vardi [AKV04] showed that the proof system of Ordered Binary Decision Diagrams with conjunction and weakening, OBDD($\land$, weakening), simulates CP* (Cutting Planes with unary coefficients). We show that OBDD($\land$, weakening) can give exponentially shorter proofs than dag-like cutting planes. This is proved by showing that the Clique-Coloring ... more >>>

TR17-117 | 20th July 2017
Dmitry Itsykson, Alexander Knop

Hard satisfiable formulas for splittings by linear combinations

Itsykson and Sokolov in 2014 introduced the class of DPLL($\oplus$) algorithms that solve Boolean satisfiability problem using the splitting by linear combinations of variables modulo 2. This class extends the class of DPLL algorithms that split by variables. DPLL($\oplus$) algorithms solve in polynomial time systems of linear equations modulo two ... more >>>

TR15-174 | 18th October 2015
Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

Complexity of distributions and average-case hardness

We address a natural question in average-case complexity: does there exist a language $L$ such that for all easy distributions $D$ the distributional problem $(L, D)$ is easy on the average while there exists some more hard distribution $D'$ such that $(L, D')$ is hard on the average? We consider ... more >>>

TR14-178 | 5th December 2014
Dmitry Itsykson, Alexander Knop, Dmitry Sokolov

Heuristic time hierarchies via hierarchies for sampling distributions

We give a new simple proof of the time hierarchy theorem for heuristic BPP originally proved by Fortnow and Santhanam [FS04] and then simplified and improved by Pervyshev [P07]. In the proof we use a hierarchy theorem for sampling distributions recently proved by Watson [W13]. As a byproduct we get ... more >>>

TR14-093 | 22nd July 2014
Dmitry Itsykson, Mikhail Slabodkin, Dmitry Sokolov

Resolution complexity of perfect mathcing principles for sparse graphs

The resolution complexity of the perfect matching principle was studied by Razborov [Raz04], who developed a technique for proving its lower bounds for dense graphs. We construct a constant degree bipartite graph $G_n$ such that the resolution complexity of the perfect matching principle for $G_n$ is $2^{\Omega(n)}$, where $n$ is ... more >>>

TR12-141 | 22nd October 2012
Dmitry Itsykson, Dmitry Sokolov

Lower bounds for myopic DPLL algorithms with a cut heuristic

The paper is devoted to lower bounds on the time complexity of DPLL algorithms that solve the satisfiability problem using a splitting strategy. Exponential lower bounds on the running time of DPLL algorithms on unsatisfiable formulas follow from the lower bounds for resolution proofs. Lower bounds on satisfiable instances are ... more >>>

TR11-091 | 20th May 2011
Edward Hirsch, Dmitry Itsykson, Valeria Nikolaenko, Alexander Smal

Optimal heuristic algorithms for the image of an injective function

The existence of optimal algorithms is not known for any decision problem in NP$\setminus$P. We consider the problem of testing the membership in the image of an injective function. We construct optimal heuristic algorithms for this problem in both randomized and deterministic settings (a heuristic algorithm can err on a ... more >>>

TR10-193 | 5th December 2010
Edward Hirsch, Dmitry Itsykson, Ivan Monakhov, Alexander Smal

On optimal heuristic randomized semidecision procedures, with applications to proof complexity and cryptography

The existence of an optimal propositional proof system is a major open question in proof complexity; many people conjecture that such systems do not exist. Krajicek and Pudlak (1989) show that this question is equivalent to the existence of an algorithm that is optimal on all propositional tautologies. Monroe (2009) ... more >>>

TR08-073 | 4th August 2008
Dmitry Itsykson

Structural complexity of AvgBPP

We study class AvgBPP that consists of distributional problems that can be solved in average polynomial time (in terms of Levin's average-case complexity) by randomized algorithms with bounded error. We prove that there exists a distributional problem that is complete for AvgBPP under polynomial-time samplable distributions. Since we use deterministic ... more >>>

TR07-117 | 8th November 2007
Edward Hirsch, Dmitry Itsykson

An infinitely-often one-way function based on an average-case assumption

We assume the existence of a function f that is computable in polynomial time but its inverse function is not computable in randomized average-case polynomial time. The cryptographic setting is, however, different: even for a weak one-way function, every possible adversary should fail on a polynomial fraction of inputs. Nevertheless, ... more >>>

TR04-041 | 18th May 2004
Michael Alekhnovich, Edward Hirsch, Dmitry Itsykson

Exponential lower bounds for the running time of DPLL algorithms on satisfiable formulas

DPLL (for Davis, Putnam, Logemann, and Loveland) algorithms form the largest family of contemporary algorithms for SAT (the propositional satisfiability problem) and are widely used in applications. The recursion trees of DPLL algorithm executions on unsatisfiable formulas are equivalent to tree-like resolution proofs. Therefore, lower bounds for tree-like resolution (which ... more >>>

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