Complexity of Dyck-reachability in directed graphs
Shankar Narayanan, Aditya
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https://hdl.handle.net/2142/110563
Description
Title
Complexity of Dyck-reachability in directed graphs
Author(s)
Shankar Narayanan, Aditya
Issue Date
2021-04-26
Director of Research (if dissertation) or Advisor (if thesis)
Viswanathan, Mahesh
Department of Study
Computer Science
Discipline
Computer Science
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
M.S.
Degree Level
Thesis
Keyword(s)
Complexity
Context-Free Language
Dyck Reachability
Graphs
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.
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