中文摘要：

参数化系统（paramterized system）是指包含特定有限状态进程多个实例的并发系统，其中的参数是指系统内进程实例的数目，即系统的规模反向可达性分析（backward reachability analysis）已被广泛用于验证参数化系统是否满足以向上封闭（upward-closed）集合表示的安全性（safety property）与有限状态系统验证相类似，参数化系统的验证同样也面临着状态爆炸（state explosion）问题，并且模型检测算法的有效性依赖于如何采用有效的数据结构表示状态集合．针对表示无穷状态的向上封闭集合，研究人员提出了多种基于约束（constraint-based）的符号表示方法．但这些方法依然面临着符号状态爆炸（symbolic state explosion）问题或者其包含判定问题，即判断一个约束条件集合符号化表示的实际状态集合是否为另一约束条件集合所对应的状态集合的子集，是Co-NP完全问题．因此，虽然有限状态验证技术能够验证一些具有一定规模的问题，但现有针对参数化系统的验证方法所能解决的问题的规模较为有限，需要近一步提高模型检测算法的效率．针对参数化系统提出了加快反向可达性分析的多个启发式规则，实验结果表明，这些启发式规则可以使算法的效率提高几个数量级，从而有助于解决现有参数化系统验证方法所存在的问题．

英文摘要：

A parameterized system is a system that involves numerous instantiations of the same finite-state process, and depends on a parameter which defines its size. The backward reachability analysis has been widely used for verifying parameterized systems against safety properties modeled as a set of upward-closed sets. As in the finite-state case, the verification of parameterized systems also faces the state explosion problem and the success of model checking depends on the data structure used for representing a set of states. Several constraint-based approaches have been proposed to symbolically represent upward-closed sets with infinite states. But those approaches are still facing the symbolic state explosion problem or the containment problem, i.e. to decide whether a set of concrete states represented by one set of constraints is a subset of another set of constraints, which is co-NP complete. As a result, those examples investigated in the literature would be considered of negligible size in finite-state model checking. This paper presents several heuristic rules specific to parameterized systems that can help to mitigate the problem. Experimental results show that the efficiency is significantly improved and the heuristic algorithm is several orders of magnitude faster than the original one in certain cases.