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Title:Complexity of Dyck-reachability in directed graphs
Author(s):Shankar Narayanan, Aditya
Advisor(s):Viswanathan, Mahesh
Department / Program:Computer Science
Discipline:Computer Science
Degree Granting Institution:University of Illinois at Urbana-Champaign
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Dyck Reachability
Abstract:We study the problem of Dyck-reachability in directed graphs de ned as follows: given a directed graph with edges labeled by either open or close parentheses, we claim that a vertex is Dyck-reachable from another if there is a path between these two vertices such that the string described by concatenating the edge labels of the path is a member of the Dyck language, i.e., the language of balanced parentheses. We present previous works on upper bounds in Dyck-reachability in graphs and the equivalent formulation of the problem in the context of Recursive State Machines. We also present known lower bounds for the Dyck-reachability problem and the conditional reduction to Boolean Matrix Multiplication as well as the k-clique problem. Finally, we give a linear-time algorithm that computes st-Dyck-reachability for graphs with bounded treewidth and using a bounded stack.
Issue Date:2021-04-26
Rights Information:Copyright 2021 Aditya Shankar Narayanan
Date Available in IDEALS:2021-09-17
Date Deposited:2021-05

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