Linear inferences and derivations 2

[This is the second of 3 emails to the Frogs list concerning linear 
inferences and derivations in deep inference. The first is about linear 
inferences that are independent of the usual basis {switch, medial}. The 
second concerns the size of linear derivations in deep inference, in the 
presence of units, and the third will present recent work towards 
efficiently automating the checking and search of new linear inferences.]

Dear all,

I would like to advertise the following note (title and abstract below):

http://www.anupamdas.com/items/LinCompDI/LinCompDI.pdf

This note forms part of ongoing work with Paula Bruscoli, Alessio 
Guglielmi and Lutz Strassburger [BGS] on the size of linear derivations 
in deep inference. In particular we focus on the situation when units 
are present, and reduce it to the case when there are no units, internal 
to the {switch, medial} system, whence better bounds can be obtained by 
the work of [BGS].

Kind regards,
Anupam

The size of linear derivations in deep inference

In unit-free deep inference it is known that derivations comprising of 
just the logical rules (switch and medial) are polynomial in size. When 
units are thrown in this picture changes drastically, as exhibited here. 
Nonetheless we show that such derivations can always be converted to 
ones of polynomial size, preserving the premiss and conclusion, without 
using structural rules.