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Electronic Colloquium on Computational Complexity

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All reports by Author Alexander Knop:

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 >>>

TR18-177 | 1st October 2018
Alexander Knop

The Diptych of Communication Complexity Classes in the Best-partition Model and the Fixed-partition Model

Most of the research in communication complexity theory is focused on the
fixed-partition model (in this model the partition of the input between
Alice and Bob is fixed). Nonetheless, the best-partition model (the model
that allows Alice and Bob to choose the partition) has a lot of
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 >>>

TR17-179 | 20th November 2017
Alexander Knop

IPS-like Proof Systems Based on Binary Decision Diagrams

It is well-known that there is equivalence between ordered resolution and ordered binary decision diagrams (OBDD) [LNNW95]; i.e., for any unsatisfiable formula ?, the size of the smallest ordered resolution refutation of ? equal to the size of the smallest OBDD for the canonical search problem corresponding to ?. But ... more >>>

TR17-176 | 15th November 2017
Kamil Khadiev, Aliya Khadiev, Alexander Knop

Exponential Separation between Quantum and Classical Ordered Binary Decision Diagrams, Reordering Method and Hierarchies

In this paper, we study quantum OBDD model, it is a restricted version of read-once quantum branching programs, with respect to "width" complexity. It is known that the maximal gap between deterministic and quantum complexities is exponential. But there are few examples of functions with such a gap. We present ... 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 >>>

TR16-119 | 1st August 2016
Alexander Golovnev, Edward Hirsch, Alexander Knop, Alexander Kulikov

On the Limits of Gate Elimination

Although a simple counting argument shows the existence of Boolean functions of exponential circuit complexity, proving superlinear circuit lower bounds for explicit functions seems to be out of reach of the current techniques. There has been a (very slow) progress in proving linear lower bounds with the latest record of ... 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 >>>

TR13-037 | 15th March 2013
Alexander Knop

Circuit Lower Bounds for Heuristic MA

Revisions: 2

Santhanam (2007) proved that MA/1 does not have circuits of size $n^k$. We translate his result to the heuristic setting by proving that there is a constant $a$ such that for any $k$, there is a language in HeurMA that cannot be solved by circuits of size $n^k$ on more ... more >>>

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