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• W2800622312 abstract "We prove that for every class $C$ of graphs with effectively bounded expansion, given a first-order sentence $varphi$ and an $n$-element structure $mathbb{A}$ whose Gaifman graph belongs to $C$, the question whether $varphi$ holds in $mathbb{A}$ can be decided by a family of AC-circuits of size $f(varphi)cdot n^c$ and depth $f(varphi)+clog n$, where $f$ is a computable function and $c$ is a universal constant. This places the model-checking problem for classes of bounded expansion in the parameterized circuit complexity class $para-AC^1$. On the route to our result we prove that the basic decomposition toolbox for classes of bounded expansion, including orderings with bounded weak coloring numbers and low treedepth decompositions, can be computed in $para-AC^1$." @default.
• W2800622312 created "2018-05-17" @default.
• W2800622312 creator A5000479623 @default.
• W2800622312 creator A5073548944 @default.
• W2800622312 creator A5085711958 @default.
• W2800622312 date "2018-05-09" @default.
• W2800622312 modified "2023-09-30" @default.
• W2800622312 title "Parameterized circuit complexity of model checking first-order logic on sparse structures" @default.
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• W2800622312 hasPublicationYear "2018" @default.
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