ﻻ يوجد ملخص باللغة العربية
In this paper we extend and prove in detail the Finite Rank Theorem for connection matrices of graph parameters definable in Monadic Second Order Logic with counting (CMSOL) from B. Godlin, T. Kotek and J.A. Makowsky (2008) and J.A. Makowsky (2009). We demonstrate its vast applicability in simplifying known and new non-definability results of graph properties and finding new non-definability results for graph parameters. We also prove a Feferman-Vaught Theorem for the logic CFOL, First Order Logic with the modular counting quantifiers.
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and rings fro
We compare the capabilities of two approaches to approximating graph isomorphism using linear algebraic methods: the emph{invertible map tests} (introduced by Dawar and Holm) and proof systems with algebraic rules, namely emph{polynomial calculus}, e
We take a graph theoretic approach to the problem of finding generators for those prime ideals of $mathcal{O}_q(mathcal{M}_{m,n}(mathbb{K}))$ which are invariant under the torus action ($mathbb{K}^*)^{m+n}$. Launois cite{launois3} has shown that the
Riordan matrices are infinite lower triangular matrices determined by a pair of formal power series over the real or complex field. These matrices have been mainly studied as combinatorial objects with an emphasis placed on the algebraic or combinato
In this paper we investigate the $lambda$ -calculus, a $lambda$-calculus enriched with resource control. Explicit control of resources is enabled by the presence of erasure and duplication operators, which correspond to thinning and con-traction rule