arXiv subjects

Nicolas de Rugy-Altherre

Publications and source records attributed to Nicolas de Rugy-Altherre.

3 recordsLinked to original sources

arXiv2021

Tractability Frontier of Data Complexity in Team Semantics

We study the data complexity of model-checking for logics with team semantics. We focus on dependence, inclusion, and independence logic formulas under both strict and lax team semantics. Our results delineate a clear tractability/intractability frontiers in data complexity of both quantifier-free and quantified formulas for each of the logics. For inclusion logic under the lax semantics, we reduce the model-checking problem to the satisfiability problem of so-called dual-Horn Boolean formulas. Via this reduction, we give an alternative proof for the known result that the data complexity of inclusion logic is in PTIME.

cs.LO↗

arXiv2013

Determinant versus Permanent: salvation via generalization? The algebraic complexity of the Fermionant and the Immanant

The fermionant can be seen as a generalization of both the permanent (for $k=-1$) and the determinant. We demonstrate that it is VNP-complete for most cases. Furthermore it is #P-complete for the cases. The immanant is also a generalization of the permanent (for a Young diagram with a single line) and of the determinant (when the Young diagram is a column). We demonstrate that the immanant of any family of Young diagrams with bounded width and at least n boxes at the right of the first column is VNP-complete.

cs.CC↗

arXiv2012

A Dichotomy Theorem for Homomorphism Polynomials

In the present paper we show a dichotomy theorem for the complexity of polynomial evaluation. We associate to each graph H a polynomial that encodes all graphs of a fixed size homomorphic to H. We show that this family is computable by arithmetic circuits in constant depth if H has a loop or no edge and that it is hard otherwise (i.e., complete for VNP, the arithmetic class related to #P). We also demonstrate the hardness over the rational field of cut eliminator, a polynomial defined by Bürgisser which is known to be neither VP nor VNP-complete in the field of two elements, if VP is not equal to VNP (VP is the class of polynomials computable by arithmetic circuit of polynomial size).

cs.CC↗