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Definability of linear equation systems over groups and rings

Anuj Dawar ; Eryk Kopczynski ; Bjarki Holm ; Erich Grädel ; Wied Pakusa.

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 from the viewpoint of logical (inter-)definability.&nbsp;[&hellip;]

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Logical properties of random graphs from small addable classes

Anuj Dawar ; Eryk Kopczyński.

We establish zero-one laws and convergence laws for monadic second-order logic (MSO) (and, a fortiori, first-order logic) on a number of interesting graph classes. In particular, we show that MSO obeys a zero-one law on the class of connected planar graphs, the class of connected graphs of&nbsp;[&hellip;]

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Bounded degree and planar spectra

Anuj Dawar ; Eryk Kopczyński.

The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexity class NE. We consider the spectra obtained by limiting models to be either planar (in the graph-theoretic sense) or by&nbsp;[&hellip;]

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