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REPORTS > KEYWORD > TSEITIN FORMULAS:
Reports tagged with Tseitin Formulas:
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 >>>

TR19-178 | 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 >>>

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 >>>

TR21-021 | 18th February 2021
Per Austrin, Kilian Risse

#### Average-Case Perfect Matching Lower Bounds from Hardness of Tseitin Formulas

We study the complexity of proving that a sparse random regular graph on an odd number of vertices does not have a perfect matching, and related problems involving each vertex being matched some pre-specified number of times. We show that this requires proofs of degree $\Omega(n/\log n)$ in the Polynomial ... more >>>

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