{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/110563"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/110563","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Complexity of Dyck-reachability in directed 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.","abstract_html":"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.","abstract_has_math":false,"creators":["Shankar Narayanan, Aditya"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"M.S.","degree_level":"Thesis","degree_discipline":"Computer Science","degree_department":null,"school":null,"contributors":["Viswanathan, Mahesh"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-09-17T01:11:16Z","date_published":"2021-09-17T01:11:16Z","updated_at":"2026-07-22T22:24:52Z","subjects":["Complexity","Context-Free Language","Dyck Reachability","Graphs"],"languages":["en"],"rights":["Copyright 2021 Aditya Shankar Narayanan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/110563","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Viswanathan, Mahesh"]},{"key":"dc:creator","label":"Author","values":["Shankar Narayanan, Aditya"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2021-09-17T01:11:16Z","2021-04-26","2021-05"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Computer Science"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.S."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Complexity","Context-Free Language","Dyck Reachability","Graphs"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2021 Aditya Shankar Narayanan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/110563"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Complexity of Dyck-reachability in directed graphs"]}]}],"canonical_facts":{"dc:contributor":["Viswanathan, Mahesh"],"dc:creator":["Shankar Narayanan, Aditya"],"dc:date":["2021-09-17T01:11:16Z","2021-04-26","2021-05"],"dc:description":["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). 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