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A note on first-order spectra with binary relations

Eryk Kopczynski ; Tony Tan.

The spectrum of a first-order sentence is the set of the cardinalities of its finite models. In this paper, we consider the spectra of sentences over binary relations that use at least three variables. We show that for every such sentence $\Phi$, there is a sentence $\Phi'$ that uses the same number&nbsp;[&hellip;]

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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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Complexity of Problems of Commutative Grammars

Eryk Kopczynski.

We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an assumption that the terminal alphabet is fixed, the membership&nbsp;[&hellip;]

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