--- _id: '5455' abstract: - lang: eng text: 'A fundamental algorithmic problem at the heart of static analysis is Dyck reachability. The input is a graphwhere the edges are labeled with different types of opening and closing parentheses, and the reachabilityinformation is computed via paths whose parentheses are properly matched. We present new results for Dyckreachability problems with applications to alias analysis and data-dependence analysis. Our main contributions,that include improved upper bounds as well as lower bounds that establish optimality guarantees, are asfollows:First, we consider Dyck reachability on bidirected graphs, which is the standard way of performing field-sensitive points-to analysis. Given a bidirected graph withnnodes andmedges, we present: (i) an algorithmwith worst-case running timeO(m+n·α(n)), whereα(n)is the inverse Ackermann function, improving thepreviously knownO(n2)time bound; (ii) a matching lower bound that shows that our algorithm is optimalwrt to worst-case complexity; and (iii) an optimal average-case upper bound ofO(m)time, improving thepreviously knownO(m·logn)bound.Second, we consider the problem of context-sensitive data-dependence analysis, where the task is to obtainanalysis summaries of library code in the presence of callbacks. Our algorithm preprocesses libraries in almostlinear time, after which the contribution of the library in the complexity of the client analysis is only linear,and only wrt the number of call sites.Third, we prove that combinatorial algorithms for Dyck reachability on general graphs with truly sub-cubic bounds cannot be obtained without obtaining sub-cubic combinatorial algorithms for Boolean MatrixMultiplication, which is a long-standing open problem. Thus we establish that the existing combinatorialalgorithms for Dyck reachability are (conditionally) optimal for general graphs. We also show that the samehardness holds for graphs of constant treewidth.Finally, we provide a prototype implementation of our algorithms for both alias analysis and data-dependenceanalysis. Our experimental evaluation demonstrates that the new algorithms significantly outperform allexisting methods on the two problems, over real-world benchmarks.' alternative_title: - IST Austria Technical Report article_processing_charge: No author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Bhavya full_name: Choudhary, Bhavya last_name: Choudhary - first_name: Andreas full_name: Pavlogiannis, Andreas id: 49704004-F248-11E8-B48F-1D18A9856A87 last_name: Pavlogiannis orcid: 0000-0002-8943-0722 citation: ama: Chatterjee K, Choudhary B, Pavlogiannis A. Optimal Dyck Reachability for Data-Dependence and Alias Analysis. IST Austria; 2017. doi:10.15479/AT:IST-2017-870-v1-1 apa: Chatterjee, K., Choudhary, B., & Pavlogiannis, A. (2017). Optimal Dyck reachability for data-dependence and alias analysis. IST Austria. https://doi.org/10.15479/AT:IST-2017-870-v1-1 chicago: Chatterjee, Krishnendu, Bhavya Choudhary, and Andreas Pavlogiannis. Optimal Dyck Reachability for Data-Dependence and Alias Analysis. IST Austria, 2017. https://doi.org/10.15479/AT:IST-2017-870-v1-1. ieee: K. Chatterjee, B. Choudhary, and A. Pavlogiannis, Optimal Dyck reachability for data-dependence and alias analysis. IST Austria, 2017. ista: Chatterjee K, Choudhary B, Pavlogiannis A. 2017. Optimal Dyck reachability for data-dependence and alias analysis, IST Austria, 37p. mla: Chatterjee, Krishnendu, et al. Optimal Dyck Reachability for Data-Dependence and Alias Analysis. IST Austria, 2017, doi:10.15479/AT:IST-2017-870-v1-1. short: K. Chatterjee, B. Choudhary, A. Pavlogiannis, Optimal Dyck Reachability for Data-Dependence and Alias Analysis, IST Austria, 2017. date_created: 2018-12-12T11:39:26Z date_published: 2017-10-23T00:00:00Z date_updated: 2023-02-21T15:54:10Z day: '23' ddc: - '000' department: - _id: KrCh doi: 10.15479/AT:IST-2017-870-v1-1 file: - access_level: open_access checksum: 177a84a46e3ac17e87b31534ad16a4c9 content_type: application/pdf creator: system date_created: 2018-12-12T11:54:02Z date_updated: 2020-07-14T12:46:59Z file_id: '5524' file_name: IST-2017-870-v1+1_main.pdf file_size: 960491 relation: main_file file_date_updated: 2020-07-14T12:46:59Z has_accepted_license: '1' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: '37' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '870' related_material: record: - id: '10416' relation: later_version status: public status: public title: Optimal Dyck reachability for data-dependence and alias analysis type: technical_report user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 year: '2017' ...