[Proof Complexity] Barnaby Martin seminar on Monday

thapen thapen at math.cas.cz
Wed Mar 24 15:41:52 CET 2021

Dear colleagues,

Barnaby Martin will give a proof complexity talk in our online logic 
seminar on Monday - see the announcement below.

To join go to
Passcode: 017107 (if required)



  Monday 29th March, 3:30pm

Speaker: Barnaby Martin, Durham University
Title: Depth lower bounds in Stabbing Planes for combinatorial 


We prove logarithmic depth lower bounds in Stabbing Planes for the 
classes of combinatorial principles known as the Pigeonhole principle 
and the Tseitin contradictions. The depth lower bounds are new, obtained 
by giving almost linear length lower bounds which do not depend on the 
bit-size of the inequalities and in the case of the Pigeonhole principle 
are tight.

The technique known so far to prove depth lower bounds for Stabbing 
Planes is a generalization of that used for the Cutting Planes proof 
system. In this work we introduce two new approaches to prove 
length/depth lower bounds in Stabbing Planes: one relying on Sperner's 
Theorem which works for the Pigeonhole principle and Tseitin 
contradictions over the complete graph; a second proving the lower bound 
for Tseitin contradictions over a grid graph, which uses a result on 
essential coverings of the boolean cube by linear polynomials, which in 
turn relies on Alon's combinatorial Nullenstellensatz.

(Joint work with Stefan Dantchev, Nicola Galesi and Abdul Ghani.)

For more information see the seminar web page at
https://calendar.math.cas.cz/logic-seminar-actual .

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