Complexity of Timeline-Based Planning

Timeline-based planning is a paradigm that models temporal planning domains as sets of independent, but interacting, components. The behavior of the components can be described by means of a number of state variables whose evolution and interactions over time are governed by a set of temporal constraints. This paradigm is different from the one underlying the common action-based formalisms à la PDDL, where the focus is on what can be done by an executive agent. Although successfully used in many real-world applications, little work has been done on the expressiveness and complexity of the timeline-based formalism. The present paper provides a characterization of the complexity of non-flexible timeline-based planning, by proving that a general formulation of the problem is EXPSPACE-complete. Such a result extends a previous work where the same complexity bound was proved for a restricted fragment of timeline-based planning that was shown to be expressive enough to capture actionbased temporal planning. In addition, we prove that requiring an upper bound to the solution horizon as part of the input decreases the complexity of the problem, that becomes NEXPTIME-complete.