In Hierarchical Task Network (HTN) planning, compound tasks need to be refined into executable (primitive) action sequences. In contrast to their primitive counterparts, compound tasks do not specify preconditions or effects. Thus, their implications on the states in which they are applied are not explicitly known: they are "hidden" in and depending on the decomposition structure. We formalize several kinds of preconditions and effects that can be inferred for compound tasks in totally ordered HTN domains. As relevant special case we introduce a problem relaxation which admits reasoning about preconditions and effects in polynomial time. We provide procedures for doing so, thereby extending previous work, which could only deal with acyclic models. We prove our procedures to be correct and complete for any totally ordered input domain. These results are embedded into an encompassing complexity analysis of the inference of preconditions and effects of compound tasks, an investigation that has not been made so far.

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We study PO and POCL plans with regard to their makespan – the execution time when allowing the parallel execution of causally independent actions. Partially ordered (PO) plans are often assumed to be equivalent to partial order causal link (POCL) plans, where the causal relationships between actions are explicitly represented via causal links. As a first contribution, we study the similarities and differences of PO and POCL plans, thereby clarifying a common misconception about their relationship: There are PO plans for which there does not exist a POCL plan with the same orderings. We prove that we can still always find a POCL plan with the same makespan in polynomial time. As another main result we prove that turning a PO or POCL plan into one with minimal makespan by only removing ordering constraints (called deordering) is NP-complete. We provide a series of further results on special cases and implications, such as reordering, where orderings can be changed arbitrarily.

In this paper we study the computational complexity of postoptimizing partially ordered plans, i.e., we investigate the problem that is concerned with detecting and deleting unnecessary actions. For totally ordered plans it can easily be tested in polynomial time whether a single action can be removed without violating executability. Identifying an executable subplan, i.e., asking whether k plan steps can be removed, is known to be NP-complete. We investigate the same questions for partially ordered input plans, as they are created by many search algorithms or used by real-world applications – in particular time-critical ones that exploit parallelism of non-conflicting actions. More formally, we investigate the computational complexity of removing an action from a partially ordered solution plan in which every linearization is a solution in the classical sense while allowing ordering insertions afterwards to repair arising executability issues. It turns out that this problem is NP-complete – even if just a single action is removed – and thereby show that this reasoning task is harder than for totally ordered plans. Moreover, we identify the structural properties responsible for this hardness by providing a fixed-parameter tractability (FPT) result.

In HTN planning the choice of decomposition methods used to refine compound tasks is key to finding a valid plan. Based on inferred preconditions and effects of compound tasks, we propose a look-ahead technique for search-based total-order HTN planning that can identify inevitable refinement choices and in some cases dead-ends. The former occurs when all but one decomposition method for some task are proven infeasible for turning a task network into a solution, whereas the latter occurs when all methods are proven infeasible. We show how it can be used for pruning, as well as to strengthen heuristics and to reduce the search branching factor. An empirical evaluation proves its potential as incorporating it improves an existing HTN planner such that it is the currently best performing one in terms of coverage and IPC score.