Nonlinear Arithmetic with SMTLIB Division is Undecidable

Computer Science > Logic in Computer Science [Submitted on 25 May 2026 (v1), last revised 3 Jun 2026 (this version, v3)] Title:Nonlinear Arithmetic with SMTLIB Division is Undecidable View PDF HTML (experimental)Abstract:We show that the nonlinear real arithmetic theory (NRA) as defined in the SMTLIB standard is undecidable. The undecidability arises from the treatment of division by zero as an uninterpreted function, which allows encoding integer arithmetic problems into NRA formulas. Submission history From: Dejan Jovanovic [view email][v1] Mon, 25 May 2026 07:27:53 UTC (4 KB) [v2] Tue, 2 Jun 2026 15:39:49 UTC (1 KB) (withdrawn) [v3] Wed, 3 Jun 2026 14:35:11 UTC (4 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.