A Complete Parameterized Complexity Analysis of Bounded Planning

The propositional planning problem is a notoriously difficult computational problem, which remains hard even under strong syntactical and structural restrictions. Given its difficulty it becomes natural to study planning in the context of parameterized complexity. In this paper we continue the work initiated by Downey, Fellows and Stege on the parameterized complexity of planning with respect to the parameter "length of the solution plan." We provide a complete classification of the parameterized complexity of the planning problem under two of the most prominent syntactical restrictions, i.e., the so called PUBS restrictions introduced by Baeckstroem and Nebel and restrictions on the number of preconditions and effects as introduced by Bylander. We also determine which of the considered fixed-parameter tractable problems admit a polynomial kernel and which don't.
Comment: The paper is a combined and extended version of the papers "The Complexity of Planning Revisited - A Parameterized Analysis" (AAAI 2012, arXiv:1208.2566) and "Parameterized Complexity and Kernel Bounds for Hard Planning Problems" (CIAC 2013, arXiv:1211.0479)