中文摘要：

对智能规划中的常用工具——放松式规划图（relaxedplanninggraph，简称RPG）的图论性质进行了深入研究．将RPG中的命题层抽取出来，得到一个不包含任何动作的命题关系图（propositionrelationgraph，简称PRO），发现PRG仍具有RPG的主要规划性质．初步研究结果包括以下4个方面：初始命题集（initialpropositionset，简称IPS）的闭出邻集（closeout．neighborhoods，简称CON）是放松式规划可达命题集（relaxedreachablepropositionset，简称R-RPS）；初始状态命题到目标状态命题的最大距离是规划解长度的合理估计；无圈序指出了对应命题被实现的顺序要求：出度或入度为1的结点收缩对应规划中构造的宏动作．上述结果中，前两者说明PRG保留RPG的主要规划性质’后两者可用于建立目标议程或宏动作提取等领域．还提出与上述结论相关的3种算法：从RPG中得到PRG的算法（复杂性为O（mn。），其中，n为RPG的命题数，m为RPG的动作数）；约简无圈序算法（复杂性为O（n＋m），其中，n为PRG的结点数，m为PRG的边数）；宏动作建议算法（复杂性为O（n2），n为PRG的结点数）．

英文摘要：

This paper focuses on graph properties of relaxed planning graph （RPG）, a widely-used tool in automated planning. When proposition levels are extracted from RPG, and thus, used to build a proposition relation graph （PRG）, it is found that PRG keeps primary planning properties in RPG. Preliminary research results include the following four aspects： The close pth out-neighborhoods （CON） of initial proposition set （IPS） is the relaxed reachable proposition set （R-RPS） in planning; the maximum distance from any proposition in initial state to any proposition in goal states is a reasonable estimation of the plan length; acyclic order in graph indicates that some orders that held corresponding propositions are necessary; contraction of in/out cut-vertex means construction of macro-action is currently being planned. The first and second results show PRG keeps planning properties in RPG and the third and fourth results can be used in goal agenda building and macro-action construction. Three related algorithms are proposed： PRG in RPG finding algorithm, an O（mn2/4） （n is the number of propositions in RPC m is the number of actions in RPG） algorithm; acyclic order reduction algorithm, an O（n＋m） （n is the number of nodes in PRG, m is the number of edges in PRG） algorithm; macro action suggestion algorithm, an O（n2） （n is the number of nodes in PRG） algorithm.