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 $\boldsymbol{\mathcal{L}}$, the $\boldsymbol{\mathcal{L}}$-definability problem for finite structures takes as an input a finite structure $\boldsymbol{A}$ and a target relation $T$ over the domain of $\boldsymbol{A}$ and determines whether there is a formula of $\boldsymbol{\mathcal{L}}$ whose interpr… Show more
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