Certifying planning systems : witnesses for unsolvability

Classical planning tackles the problem of finding a sequence of actions that leads from an initial state to a goal. Over the last decades, planning systems have become significantly better at answering the question whether such a sequence exists by applying a variety of techniques which have become more and more complex. As a result, it has become nearly impossible to formally analyze whether a planning system is actually correct in its answers, and we need to rely on experimental evidence.
One way to increase trust is the concept of certifying algorithms, which provide a witness which justifies their answer and can be verified independently. When a planning system finds a solution to a problem, the solution itself is a witness, and we can verify it by simply applying it. But what if the planning system claims the task is unsolvable? So far there was no principled way of verifying this claim.
This thesis contributes two approaches to create witnesses for unsolvable planning tasks. Inductive certificates are based on the idea of invariants. They argue that the initial state is part of a set of states that we cannot leave and that contains no goal state. In our second approach, we define a proof system that proves in an incremental fashion that certain states cannot be part of a solution until it has proven that either the initial state or all goal states are such states.
Both approaches are complete in the sense that a witness exists for every unsolvable planning task, and can be verified efficiently (in respect to the size of the witness) by an independent verifier if certain criteria are met. To show their applicability to state-of-the-art planning techniques, we provide an extensive overview how these approaches can cover several search algorithms, heuristics and other techniques. Finally, we show with an experimental study that generating and verifying these explanations is not only theoretically possible but also practically feasible, thus making a first step towards fully certifying planning systems.