[2210.09899] First Order Logic on Pathwidth Revisited Again Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Data Structures and Algorithms arXiv:2210.09899 (cs) [Submitted on 18 Oct 2022 ( v1 ), last revised 10 Jun 2026 (this version, v5)] Title: First Order Logic on Pathwidth Revisited Again Authors: Michael Lampis View a PDF of the paper titled First Order Logic on Pathwidth Revisited Again, by Michael Lampis View PDF HTML (experimental) Abstract: Courcelle's celebrated theorem states that all MSO-expressible properties can be decided in linear time on graphs of bounded treewidth. Unfortunately, the hidden constant implied by this theorem is a tower of exponentials whose height increases with each quantifier alternation in the formula. More devastatingly, this cannot be improved, under standard assumptions, even if we consider the much more restricted problem of deciding FO-expressible properties on trees. In this paper we revisit this well-studied topic and identify a natural special case where the dependence of Courcelle's theorem can, in fact, be improved. Specifically, we show that all FO-expressible properties can be decided with an elementary dependence on the input formula, if the input graph has bounded pathwidth (rather than treewidth). This is a rare example of treewidth and pathwidth having different complexity behaviors. Our result is also in sharp contrast with MSO logic on graphs of bounded pathwidth, where it is known that the dependence has to be non-elementary, under standard assumptions. Our work builds upon, and generalizes, a corresponding meta-theorem by Gajarský and Hliněný for the more restricted class of graphs of bounded tree-depth. Subjects: Data Structures and Algorithms (cs.DS) ; Computational Complexity (cs.CC); Logic in Computer Science (cs.LO) Cite as: arXiv:2210.09899 [cs.DS] (or arXiv:2210.09899v5 [cs.DS] for this version) https://doi.org/10.48550/arXiv.2210.09899 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Logical Methods in Computer Science, Volume 22, Issue 2 (June 11, 2026) lmcs:12677 Related DOI : https://doi.org/10.46298/lmcs-22%282%3A26%292026 Focus to learn more DOI(s) linking to related resources Submission history From: Michael Lampis [ view email ] [via LMCS proxy] [v1] Tue, 18 Oct 2022 14:41:26 UTC (170 KB) [v2] Wed, 20 Aug 2025 14:49:40 UTC (113 KB) [v3] Mon, 30 Mar 2026 09:10:43 UTC (111 KB) [v4] Thu, 30 Apr 2026 20:45:38 UTC (109 KB) [v5] Wed, 10 Jun 2026 17:49:22 UTC (112 KB) Full-text links: Access Paper: View a PDF of the paper titled First Order Logic on Pathwidth Revisited Again, by Michael Lampis View PDF HTML (experimental) TeX Source view license Current browse context: cs.DS < prev | next > new | recent | 2022-10 Change to browse by: cs cs.CC cs.LO References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from