Structurally Restricted Fragments of Numeric Planning – a Complexity Analysis

Alexander Shleyfman, Daniel Gnad, Peter Jonsson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


Numeric planning is known to be undecidable even under severe restrictions. Prior work has investigated the decidability boundaries by restricting the expressiveness of the planning formalism in terms of the numeric functions allowed in conditions and effects. We study a well-known restricted form of Hoffmann’s simple numeric planning, which is undecidable. We analyze the complexity by imposing restrictions on the causal structure, exploiting a novel method for bounding variable domain sizes. First, we show that plan existence for tasks where all numeric variables are root nodes in the causal graph is in PSPACE. Second, we show that for tasks with only numeric leaf variables the problem is decidable, and that it is in PSPACE if the propositional state space has a fixed size. Our work lays a strong foundation for future investigations of structurally more complex tasks. From a practical perspective, our method allows to employ heuristics and methods that are geared towards finite variable domains (such as pattern database heuristics or decoupled search) to solve non-trivial families of numeric planning problems.

Original languageEnglish
Title of host publicationAAAI-23 Technical Tracks 10
EditorsBrian Williams, Yiling Chen, Jennifer Neville
PublisherAAAI press
Number of pages8
ISBN (Electronic)9781577358800
StatePublished - 27 Jun 2023
Event37th AAAI Conference on Artificial Intelligence, AAAI 2023 - Washington, United States
Duration: 7 Feb 202314 Feb 2023

Publication series

NameProceedings of the 37th AAAI Conference on Artificial Intelligence, AAAI 2023


Conference37th AAAI Conference on Artificial Intelligence, AAAI 2023
Country/TerritoryUnited States

Bibliographical note

Publisher Copyright:
Copyright © 2023, Association for the Advancement of Artificial Intelligence ( All rights reserved.


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