Near-Optimal Lower Bounds on Regular Resolution Refutations of Tseitin Formulas for All Constant-Degree Graphs

2021 ◽  
Vol 30 (2) ◽  
Author(s):  
Dmitry Itsykson ◽  
Artur Riazanov ◽  
Danil Sagunov ◽  
Petr Smirnov
Keyword(s):  
Lower Bounds ◽  
Constant Degree

Lower Bounds on OBDD Proofs with Several Orders

2021 ◽  
Vol 22 (4) ◽  
pp. 1-30
Author(s):  
Sam Buss ◽  
Dmitry Itsykson ◽  
Alexander Knop ◽  
Artur Riazanov ◽  
Dmitry Sokolov
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Communication Complexity ◽  
Multiparty Communication ◽  
Constant Degree ◽  
Polynomial Size ◽  
Explicit Constant ◽  
Open Question ◽  
System 1 ◽  
Exponential Size

This article is motivated by seeking lower bounds on OBDD(∧, w, r) refutations, namely, OBDD refutations that allow weakening and arbitrary reorderings. We first work with 1 - NBP ∧ refutations based on read-once nondeterministic branching programs. These generalize OBDD(∧, r) refutations. There are polynomial size 1 - NBP(∧) refutations of the pigeonhole principle, hence 1-NBP(∧) is strictly stronger than OBDD}(∧, r). There are also formulas that have polynomial size tree-like resolution refutations but require exponential size 1-NBP(∧) refutations. As a corollary, OBDD}(∧, r) does not simulate tree-like resolution, answering a previously open question. The system 1-NBP(∧, ∃) uses projection inferences instead of weakening. 1-NBP(∧, ∃ k is the system restricted to projection on at most k distinct variables. We construct explicit constant degree graphs G n on n vertices and an ε > 0, such that 1-NBP(∧, ∃ ε n ) refutations of the Tseitin formula for G n require exponential size. Second, we study the proof system OBDD}(∧, w, r ℓ ), which allows ℓ different variable orders in a refutation. We prove an exponential lower bound on the complexity of tree-like OBDD(∧, w, r ℓ ) refutations for ℓ = ε log n , where n is the number of variables and ε > 0 is a constant. The lower bound is based on multiparty communication complexity.

scholarly journals Correction to: Near-Optimal Lower Bounds on Regular Resolution Refutations of Tseitin Formulas for All Constant-Degree Graphs

2021 ◽  
Vol 30 (2) ◽  
Author(s):  
Dmitry Itsykson ◽  
Artur Riazanov ◽  
Danil Sagunov ◽  
Petr Smirnov
Keyword(s):  
Lower Bounds ◽  
Constant Degree

scholarly journals Lower bounds for constant degree independent sets

1994 ◽  
Vol 127 (1-3) ◽  
pp. 15-21 ◽  
Author(s):  
Michael O. Albertson ◽  
Debra L. Boutin
Keyword(s):  
Lower Bounds ◽  
Independent Sets ◽  
Constant Degree

Lower Bounds in Communication Complexity

2007 ◽  
Author(s):  
T. Lee ◽  
A. Shraibman
Keyword(s):  
Lower Bounds ◽  
Communication Complexity

Two Lower Bounds for Shortest Double-Base Number System

2015 ◽  
Vol E98.A (6) ◽  
pp. 1310-1312 ◽  
Author(s):  
Parinya CHALERMSOOK ◽  
Hiroshi IMAI ◽  
Vorapong SUPPAKITPAISARN
Keyword(s):  
Lower Bounds ◽  
Number System ◽  
Base Number ◽  
Double Base

Lower bounds on the dimension of the Rauzy gasket

2020 ◽  
Vol 148 (2) ◽  
pp. 321-327
Author(s):  
Rodolfo Gutiérrez-Romo ◽  
Carlos Matheus
Keyword(s):  
Lower Bounds

A Lower Bound for Schur Numbers and Multicolor Ramsey Numbers

10.37236/1188 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Geoffrey Exoo
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Ramsey Numbers

For $k \geq 5$, we establish new lower bounds on the Schur numbers $S(k)$ and on the k-color Ramsey numbers of $K_3$.

Sign in / Sign up

Export Citation Format

Share Document