An Efficient Algorithm for Solving the Dyck-CFL Reachability Problem on Trees

The context-free language (CFL) reachability problem is well known and studied in computer science, as a fundamental problem underlying many important static analyses such as points-to-analysis. Solving the CFL reachability problem in the general case is very hard. Popular solutions resorting to a graph traversal exhibit a time complexity of O(k3 n3 ) for a grammar of size k. For Dyck CFLs, a particular class of CFLs, this complexity can be reduced to O(kn3 ). Only recently the first subcubic algorithm was proposed by Chaudhuri, dividing the complexity of predating solutions by a factor of log n. In this paper we propose an effective algorithm for solving the CFL reachability problem for Dyck languages when the considered graph is a bidirected tree with specific constraints. Our solution pre-processes the graph in O(n log n log k) time in a space of O(n log n), after which any DyckCFL reachability query can be answered in O(1) time, while a na

• Type: Conference
• Year: 2009
• Where: ESOP
• Authors: Hao Yuan, Patrick Th. Eugster
• Keywords: CFL Reachability Problem, DyckCFL Reachability Query, ESOP 2009, Programming Languages, Reachability Problem