Lower Bounds for Lovász–Schrijver Systems and Beyond Follow from Multiparty Communication Complexity

2007 ◽  
Vol 37 (3) ◽  
pp. 845-869 ◽  
Author(s):  
Paul Beame ◽  
Toniann Pitassi ◽  
Nathan Segerlind
Keyword(s):  
Lower Bounds ◽  
Communication Complexity ◽  
Multiparty Communication

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 Lower Bounds for Number-in-Hand Multiparty Communication Complexity, Made Easy

2016 ◽  
Vol 45 (1) ◽  
pp. 174-196 ◽  
Author(s):  
Jeff M. Phillips ◽  
Elad Verbin ◽  
Qin Zhang
Keyword(s):  
Lower Bounds ◽  
Communication Complexity ◽  
Multiparty Communication

Quantum multiparty communication complexity and circuit lower bounds

2009 ◽  
Vol 19 (1) ◽  
pp. 119-132 ◽  
Author(s):  
IORDANIS KERENIDIS
Keyword(s):  
Lower Bounds ◽  
Communication Complexity ◽  
Quantum Model ◽  
Multiparty Communication ◽  
Circuit Lower Bounds ◽  
Quantum Models ◽  
Open Question

We define a quantum model for multiparty communication complexity and prove a simulation theorem between the classical and quantum models. As a result, we show that if the quantum k-party communication complexity of a function f is Ω(n/2k), its classical k-party communication is Ω(n/2k/2). Finding such an f would allow us to prove strong classical lower bounds for k ≥ log n players and make progress towards solving a major open question about symmetric circuits.

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