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Mathematical Problems in Engineering
Volume 2013, Article ID 398245, 6 pages
Research Article

On the Completeness of Pruning Techniques for Planning with Conditional Effects

1School of Computer Science and Engineering, Wuhan Institute of Technology, Wuhan 430205, China
2Hubei Province Key Laboratory of Intelligent Robot, Wuhan Institute of Technology, Wuhan 430205, China

Received 18 May 2013; Accepted 17 July 2013

Academic Editor: William Guo

Copyright © 2013 Dunbo Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Pruning techniques and heuristics are two keys to the heuristic search-based planning. The helpful actions pruning (HAP) strategy and relaxed-plan-based heuristics are two representatives among those methods and are still popular in the state-of-the-art planners. Here, we present new analyses on the properties of HAP. Specifically, we show new reasons for which HAP can cause incompleteness of a search procedure. We prove that, in general, HAP is incomplete for planning with conditional effects if factored expansions of actions are used. To preserve completeness, we propose a pruning strategy that is based on relevance analysis and confrontation. We will show that both relevance analysis and confrontation are necessary. We call it the confrontation and goal relevant actions pruning (CGRAP) strategy. However, CGRAP is computationally hard to be exactly computed. Therefore, we suggest practical approximations from the literature.