2026-09-20T17:40:38Z https://www.ideals.illinois.edu/oai-pmh

oai:www.ideals.illinois.edu:2142/110563 2023-07-11 col_2142_5131 col_2142_10761 com_2142_5130 com_2142_10755 com_2142_234

Viswanathan, Mahesh Shankar Narayanan, Aditya 2021-09-17T01:11:16Z 2021-09-17T01:11:16Z 2021-04-26 2021-05 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. Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2021-09-16 without embargo terms The student, Aditya Shankar Narayanan, accepted the attached license on 2021-04-23 at 12:14. The student, Aditya Shankar Narayanan, submitted this Thesis for approval on 2021-04-23 at 12:26. This Thesis was approved for publication on 2021-04-26 at 15:21. DSpace SAF Submission Ingestion Package generated from Vireo submission #16528 on 2021-09-16 at 16:47:25 Made available in DSpace on 2021-09-17T01:11:16Z (GMT). No. of bitstreams: 2 SHANKARNARAYANAN-THESIS-2021.pdf: 597194 bytes, checksum: 234efd65642c73d1d6f60d805ab1b322 (MD5) LICENSE.txt: 4221 bytes, checksum: b8d3cb67e791ed4d6c6c7b8605b95b85 (MD5) Previous issue date: 2021-04-26 application/pdf http://hdl.handle.net/2142/110563 en Copyright 2021 Aditya Shankar Narayanan Complexity Context-Free Language Dyck Reachability Graphs Complexity of Dyck-reachability in directed graphs text Thesis Computer Science Computer Science University of Illinois at Urbana-Champaign Thesis M.S.