FLOC 2018: FEDERATED LOGIC CONFERENCE 2018
Parameterized circuit complexity of model-checking on sparse structures

Authors: Michał Pilipczuk, Sebastian Siebertz and Szymon Toruńczyk

Paper Information

Title:Parameterized circuit complexity of model-checking on sparse structures
Authors:Michał Pilipczuk, Sebastian Siebertz and Szymon Toruńczyk
Proceedings:LICS PDF files
Editors: Anuj Dawar and Erich Grädel
Keywords:Model-checking first-order logic, Circuit complexity, Bounded expansion
Abstract:

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 $A$ whose Gaifman graph belongs to $C$, the question whether $\varphi$ holds in $A$ can be decided by a family of AC-circuits of size $f(\varphi)\cdot n^c$ and depth $f(\varphi)+c\log n$, 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 $paraAC^1$. 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 $paraAC^1$.

Pages:10
Talk:Jul 09 11:20 (Session 47D)
Paper: