An Analysis of the Decidability and Complexity of Numeric Additive Planning

Hayyan Helal, Gerhard Lakemeyer

Keywords: Action-based planning, Numeric planning, Planning as search, Integer linear programming.

TL;DR: By analyzing the minimal required number of action repetition, decidable fragments of numeric planning can be defined.

Abstract: In this paper, we first define numeric additive planning ($\mathrm{NAP}$), a planning formulation equivalent to Hoffmann's Restricted Tasks over Integers. Then, we analyze the minimal number of action repetitions required for a solution, since planning turns out to be decidable as long as such numbers can be calculated for all actions. We differentiate between two kinds of repetitions and solve for one by integer linear programming and the other by search. Additionally, we characterize the differences between propositional planning and $\mathrm{NAP}$ regarding these two kinds. To achieve this, we define so-called multi-valued partial order plans, a novel compact plan representation. Finally, we consider decidable fragments of $\mathrm{NAP}$ and their complexity.

Primary Keywords: Theory

Category: Long

Student: Graduate

Submission Number: 255