Solving "pseudo-injective" polynomial equations over finite dynamical systems

[2504.06986] Solving "pseudo-injective" polynomial equations over finite dynamical systems Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Discrete Mathematics arXiv:2504.06986 (cs) [Submitted on 9 Apr 2025 ( v1 ), last revised 2 Sep 2025 (this version, v2)] Title: Solving "pseudo-injective" polynomial equations over finite dynamical systems Authors: Antonio E. Porreca , Marius Rolland View a PDF of the paper titled Solving "pseudo-injective" polynomial equations over finite dynamical systems, by Antonio E. Porreca and Marius Rolland View PDF HTML (experimental) Abstract: We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient algorithms for solving polynomial equations of the form $P(X) = B$, with a constant side B, with the goal of decomposing complex behaviors into simpler systems. Taking inspiration from the characterization of injective polynomials P over dynamical systems, which is based on a condition on the lengths of limit cycles of their coefficients, we introduce a more general notion of pseudo-injectivity by relaxing this constraint. We prove that the associated equations can be solved efficiently, even in certain cases where the input is encoded in an exponentially more compact way. Subjects: Discrete Mathematics (cs.DM) ; Dynamical Systems (math.DS) Cite as: arXiv:2504.06986 [cs.DM] (or arXiv:2504.06986v2 [cs.DM] for this version) https://doi.org/10.48550/arXiv.2504.06986 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.1007/978-3-032-01570-9_12 Focus to learn more DOI(s) linking to related resources Submission history From: Marius Rolland [ view email ] [v1] Wed, 9 Apr 2025 15:49:39 UTC (143 KB) [v2] Tue, 2 Sep 2025 07:26:21 UTC (131 KB) Full-text links: Access Paper: View a PDF of the paper titled Solving "pseudo-injective" polynomial equations over finite dynamical systems, by Antonio E. Porreca and Marius Rolland View PDF HTML (experimental) TeX Source view license Current browse context: cs.DM < prev | next > new | recent | 2025-04 Change to browse by: cs math math.DS 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

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