While it is easy to verify that an action sequence is a solution for a classical planning task, there is no such verification capability if a task is reported unsolvable. We are therefore interested in certificates that allow an independent verification of the absence of solutions. We identify promising concepts for certificates that can be generated by a wide range of planning approaches. We p...

We give the first linear-time certifying algorithms to recognize trivially perfect graphs, with sublinear certificates for negative output. In case of membership in the class of trivially perfect graphs, our algorithms provide as certificate a structure for the input graph that characterizes the class, and in case of non-membership they provide as certificate a forbidden induced subgraph of the...

In this paper, we present sparse certificates for biconnectivity together with algorithms for updating these certificates. We thus obtain fully-dynamic algorithms for biconnectivity in graphs that run in O( √ n log n logdn e) amortized time per operation, where m is the number of edges and n is the number of nodes in the graph. This improves upon the results in [12], in which algorithms were pr...