## 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: |