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- W2939776956 abstract "In this article we formally define and investigate the computational complexity of the Definability Problem for open first-order formulas (i.e., quantifier free first-order formulas) with equality. Given a logic $mathbf{mathcal{L}}$, the $mathbf{mathcal{L}}$-Definability Problem for finite structures takes as input a finite structure $mathbf{A}$ and a target relation $T$ over the domain of $mathbf{A}$, and determines whether there is a formula of $mathbf{mathcal{L}}$ whose interpretation in $mathbf{A}$ coincides with $T$. We show that the complexity of this problem for open first-order formulas (open definability, for short) is coNP-complete. We also investigate the parametric complexity of the problem, and prove that if the size and the arity of the target relation $T$ are taken as parameters then open definability is $mathrm{coW}[1]$-complete for every vocabulary $tau$ with at least one, at least binary, relation." @default.
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- W2939776956 date "2019-04-09" @default.
- W2939776956 modified "2023-10-01" @default.
- W2939776956 title "The Complexity of Definability by Open First-Order Formulas" @default.
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