Is This Plan Necessarily Redundant? On the Computational Complexity of Unobserved Domain Learning

Domain learning is the task of inferring actions' preconditions and effects (domains) from executed sequences of actions (plans) along with a varying detail of information about the corresponding world states. Remarkably, even if the state remains completely unobserved, as in this work, we can infer the existence of certain state features if we assume that the plans we learn from are non-redundant. Moreover, plans might be redundant regardless of the underlying domain. We study the computational complexity of deciding whether there exists a domain in which a given plan is justified in the sense that either no single action (well-justification) or no set of actions (perfect justification) can be removed without violating correctness of the plan. We allow either arbitrarily large domains or domains with a polynomial bound on the number of state variables. We show that the problem is in P for well-justified plans and arbitrary domains, NP-complete for well-justified plans and bounded domains, in coNP for perfectly justified plans and arbitrary domains, and in Σ₂^p for perfectly justified plans and bounded domains.