All reports by Author Ricard Gavaldà:

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TR05-059
| 9th May 2005
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Víctor Dalmau, Ricard Gavaldà, Pascal Tesson, Denis Thérien#### Tractable Clones of Polynomials over Semigroups

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TR00-008
| 20th January 2000
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Albert Atserias, Nicola Galesi, Ricard Gavaldà#### Monotone Proofs of the Pigeon Hole Principle

Víctor Dalmau, Ricard Gavaldà, Pascal Tesson, Denis Thérien

It is well known that coset-generating relations lead to tractable

constraint satisfaction problems. These are precisely the relations closed

under the operation $xy^{-1}z$ where the multiplication is taken in

some finite group. Bulatov et al. have on the other hand shown that

any clone containing the multiplication of some ``block-group'' ...
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Albert Atserias, Nicola Galesi, Ricard Gavaldà

We study the complexity of proving the Pigeon Hole

Principle (PHP) in a monotone variant of the Gentzen Calculus, also

known as Geometric Logic. We show that the standard encoding

of the PHP as a monotone sequent admits quasipolynomial-size proofs

in this system. This result is a consequence of ...
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