Complexity of Dyck-reachability in directed graphs

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.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2021

Author dc:creator

• Shankar Narayanan, Aditya

Contributors dc:contributor

• Viswanathan, Mahesh

• Complexity
• Context-Free Language
• Dyck Reachability
• Graphs

Statement dc:rights

• Copyright 2021 Aditya Shankar Narayanan

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/110563

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/110563