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Preservation and decomposition theorems for bounded degree structures

Frederik Harwath ; Lucas Heimberg ; Nicole Schweikardt.

We provide elementary algorithms for two preservation theorems for first-order sentences (FO) on the class \^ad of all finite structures of degree at most d: For each FO-sentence that is preserved under extensions (homomorphisms) on \^ad, a \^ad-equivalent existential (existential-positive)&nbsp;[&hellip;]

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The succinctness of first-order logic on linear orders

Martin Grohe ; Nicole Schweikardt.

Succinctness is a natural measure for comparing the strength of different logics. Intuitively, a logic L_1 is more succinct than another logic L_2 if all properties that can be expressed in L_2 can be expressed in L_1 by formulas of (approximately) the same size, but some properties can be expressed&nbsp;[&hellip;]

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Enumerating Answers to First-Order Queries over Databases of Low Degree

Arnaud Durand ; Nicole Schweikardt ; Luc Segoufin.

A class of relational databases has low degree if for all $\delta>0$, all but finitely many databases in the class have degree at most $n^{\delta}$, where $n$ is the size of the database. Typical examples are databases of bounded degree or of degree bounded by $\log n$. It is known that over a&nbsp;[&hellip;]

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