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Electronic Colloquium on Computational Complexity

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Reports tagged with counting quantifiers:
TR06-014 | 20th December 2005
Argimiro Arratia, Carlos E. Ortiz

On a syntactic approximation to logics that capture complexity classes

We formulate a formal syntax of approximate formulas for the logic with counting
quantifiers, $\mathcal{SOLP}$, studied by us in \cite{aaco06}, where we showed the
following facts:
$(i)$ In the presence of a built--in (linear) order, $\mathcal{SOLP}$ can
describe {\bf NP}--complete problems and fragments of it capture classes like
{\bf P} ... more >>>

TR11-077 | 8th May 2011
Albert Atserias, Elitza Maneva

Graph Isomorphism, Sherali-Adams Relaxations and Expressibility in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the notion of fractional isomorphism. We show ... more >>>

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