--- _id: '5441' abstract: - lang: eng text: We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the one-time preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the best-known graph algorithm on the product. In this approach, even the answer to a single query requires the transitive closure (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time. Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time, each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results showing that the worst-case running time of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (i.e., improving the worst-case bound for the shortest path problem in general graphs). Preliminary experimental results show that our algorithms perform favorably on several benchmarks. alternative_title: - IST Austria Technical Report author: - first_name: Krishnendu full_name: Chatterjee, Krishnendu id: 2E5DCA20-F248-11E8-B48F-1D18A9856A87 last_name: Chatterjee orcid: 0000-0002-4561-241X - first_name: Rasmus full_name: Ibsen-Jensen, Rasmus id: 3B699956-F248-11E8-B48F-1D18A9856A87 last_name: Ibsen-Jensen orcid: 0000-0003-4783-0389 - first_name: Amir full_name: Goharshady, Amir id: 391365CE-F248-11E8-B48F-1D18A9856A87 last_name: Goharshady orcid: 0000-0003-1702-6584 - 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, Ibsen-Jensen R, Goharshady AK, Pavlogiannis A. Algorithms for Algebraic Path Properties in Concurrent Systems of Constant Treewidth Components. IST Austria; 2015. doi:10.15479/AT:IST-2015-340-v1-1 apa: Chatterjee, K., Ibsen-Jensen, R., Goharshady, A. K., & Pavlogiannis, A. (2015). Algorithms for algebraic path properties in concurrent systems of constant treewidth components. IST Austria. https://doi.org/10.15479/AT:IST-2015-340-v1-1 chicago: Chatterjee, Krishnendu, Rasmus Ibsen-Jensen, Amir Kafshdar Goharshady, and Andreas Pavlogiannis. Algorithms for Algebraic Path Properties in Concurrent Systems of Constant Treewidth Components. IST Austria, 2015. https://doi.org/10.15479/AT:IST-2015-340-v1-1. ieee: K. Chatterjee, R. Ibsen-Jensen, A. K. Goharshady, and A. Pavlogiannis, Algorithms for algebraic path properties in concurrent systems of constant treewidth components. IST Austria, 2015. ista: Chatterjee K, Ibsen-Jensen R, Goharshady AK, Pavlogiannis A. 2015. Algorithms for algebraic path properties in concurrent systems of constant treewidth components, IST Austria, 24p. mla: Chatterjee, Krishnendu, et al. Algorithms for Algebraic Path Properties in Concurrent Systems of Constant Treewidth Components. IST Austria, 2015, doi:10.15479/AT:IST-2015-340-v1-1. short: K. Chatterjee, R. Ibsen-Jensen, A.K. Goharshady, A. Pavlogiannis, Algorithms for Algebraic Path Properties in Concurrent Systems of Constant Treewidth Components, IST Austria, 2015. date_created: 2018-12-12T11:39:21Z date_published: 2015-07-11T00:00:00Z date_updated: 2023-09-19T14:36:19Z day: '11' ddc: - '000' department: - _id: KrCh doi: 10.15479/AT:IST-2015-340-v1-1 file: - access_level: open_access checksum: df383dc62c94d7b2ea639aba088a76c6 content_type: application/pdf creator: system date_created: 2018-12-12T11:54:09Z date_updated: 2020-07-14T12:46:56Z file_id: '5531' file_name: IST-2015-340-v1+1_main.pdf file_size: 861396 relation: main_file file_date_updated: 2020-07-14T12:46:56Z has_accepted_license: '1' language: - iso: eng month: '07' oa: 1 oa_version: Published Version page: '24' publication_identifier: issn: - 2664-1690 publication_status: published publisher: IST Austria pubrep_id: '340' related_material: record: - id: '1437' relation: later_version status: public - id: '5442' relation: earlier_version status: public - id: '6009' relation: later_version status: public status: public title: Algorithms for algebraic path properties in concurrent systems of constant treewidth components type: technical_report user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2015' ...