A Dynamic Epistemic Framework for Conformant Planning

In this paper, we introduce a lightweight dynamic epistemic logical framework for automated planning under initial uncertainty. We reduce plan verification and conformant planning to model checking problems of our logic. We show that the model checking problem of the iteration-free fragment is PSPACE-complete. By using two non-standard (but equivalent) semantics, we give novel model checking algorithms to the full language and the iteration-free language.Comment: In Proceedings TARK 2015, arXiv:1606.0729

Vertex-Coloring 2-Edge-Weighting of Graphs

A $k$-{\it edge-weighting} $w$ of a graph $G$ is an assignment of an integer weight, $w(e)\in \{1,\dots, k\}$, to each edge $e$. An edge weighting naturally induces a vertex coloring $c$ by defining $c(u)=\sum_{u\sim e} w(e)$ for every $u \in V(G)$. A $k$-edge-weighting of a graph $G$ is \emph{vertex-coloring} if the induced coloring $c$ is proper, i.e., $c(u) \neq c(v)$ for any edge $uv \in E(G)$. Given a graph $G$ and a vertex coloring $c_0$, does there exist an edge-weighting such that the induced vertex coloring is $c_0$? We investigate this problem by considering edge-weightings defined on an abelian group. It was proved that every 3-colorable graph admits a vertex-coloring $3$-edge-weighting \cite{KLT}. Does every 2-colorable graph (i.e., bipartite graphs) admit a vertex-coloring 2-edge-weighting? We obtain several simple sufficient conditions for graphs to be vertex-coloring 2-edge-weighting. In particular, we show that 3-connected bipartite graphs admit vertex-coloring 2-edge-weighting