Relational Kleene algebra with graph loop has a PSPACE-complete equational theory over relational models.
Graph structure and monadic second-order logic, a language theoretic approach, Cambridge University Press
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MSO transduction recovers the laminar tree from a laminar set system, resolving Courcelle's question and enabling MSO constructions for modular, split, and bi-join decompositions.
Tree-to-tree Hennie machines compute functions with linear size-to-height increase that lie between LSHI macro tree transducers and MSO set interpretations, are closed under specific compositions, contain the strict linear-height MTT composition hierarchy, and are equivalently characterized by a lin
Fair MSO1 problems are W[1]-hard parameterized by cluster vertex deletion in general, but admit FPT algorithms under a sufficient condition that includes fair feedback vertex set, vertex cover, dominating set, and odd cycle transversal.
CMSO-transductions are given for the modular, split and bi-join decompositions of graphs, plus a generalization to weakly-partitive set systems.
Generalizes graph coverings and unfoldings to weighted versions, proves analogous theorems to Leighton-Norris, and obtains a canonical factorization of universal coverings plus a weighted version of characteristic polynomial factorization.
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