All reports by Author Artur Riazanov:

__
TR22-046
| 4th April 2022
__

Dmitry Itsykson, Artur Riazanov#### Automating OBDD proofs is NP-hard

__
TR20-184
| 10th December 2020
__

Dmitry Itsykson, Artur Riazanov#### Proof complexity of natural formulas via communication arguments

__
TR20-073
| 5th May 2020
__

Sam Buss, Dmitry Itsykson, Alexander Knop, Artur Riazanov, Dmitry Sokolov#### Lower Bounds on OBDD Proofs with Several Orders

__
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

__
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

Dmitry Itsykson, Artur Riazanov

We prove that the proof system OBDD(and, weakening) is not automatable unless P = NP. The proof is based upon the celebrated result of Atserias and Muller [FOCS 2019] about the hardness of automatability for resolution. The heart of the proof is lifting with a multi-output indexing gadget from resolution ... more >>>

Dmitry Itsykson, Artur Riazanov

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 >>>

Sam Buss, Dmitry Itsykson, Alexander Knop, Artur Riazanov, Dmitry Sokolov

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 >>>

Dmitry Itsykson, Artur Riazanov, Danil Sagunov, Petr Smirnov

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 >>>

Nicola Galesi, Dmitry Itsykson, Artur Riazanov, Anastasia Sofronova

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 >>>