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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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