How hard can it be? The computational complexity of planning


Understanding the computational complexity of a problem is one of the first steps to understand the problem deeply. Automated planning problems are not an exception, and indeed the complexity of planning is a well studied topic in the literature of the field.

Most people in the planning community are familiar with the seminal result by Bylander showing that classical STRIPS planning is PSPACE-complete, but the topic is far from being exhausted by this result. Different kinds of planning problems, such as temporal, timeline-based, FOND, conformant or numeric planning, have been studied to prove their complexity and, in some cases, their undecidability. The resulting picture is unexpectedly jagged and interesting, and sheds light over the nature of these problems and of the algorithmic techniques that one can hope to find to solve them.

This tutorial provides an introduction and a thorough overview of the computational complexity of many kinds of planning problems, of the techniques used to prove such complexity results, and of some implications of these results to the practice of automated planning. The tutorial will not be a flat list of results and proofs, but aims to give a broad intuition of the results, their reason and implications, while going technical when needed.

The tutorial is targeted both at novices that want to obtain a solid theoretical background of the field, and to experienced researchers aiming at an up-to-date picture of the topic. A basic background on complexity theory will be refreshed as needed.


Here is a tentative outline of the tutorial:

  • Introduction and complexity theory background
  • The classics: complexity of classical STRIPS and PDDL
  • Inside PSPACE: compilability of propositional planning formalisms
  • The very hard case: undecidability of numeric planning
  • Temporal planning
    • complexity over discrete time
    • complexity and undecidable cases over dense time
    • timeline-based planning
  • Interacting with the world
    • conformant planning
    • FOND planning
  • Concluding remarks


Nicola Gigante

Nicola got his PhD at the University of Udine, Italy with a thesis on the theoretical foundations of timeline-based planning. Now he is a researcher at the Free University of Bozen-Bolzano, Italy, working on temporal reasoning in the broadest sense, including temporal planning but also temporal logics and reactive synthesis.