{
  "abstract": "This paper presents a dual-algebraic framework for control barrier functions (CBFs) that guarantees deterministic execution using exclusively elementary arithmetic. We develop this deterministic approach to solve a fundamental bottleneck in safety-critical control: pointwise minima compose intersecting safe sets, but generate non-smooth boundaries where standard Lie derivatives fail. Existing mathematical workarounds inject approximation bias, probabilistic non-determinism, or combinatorial execution delays that impede hard real-time hardware certification. By embedding the system state and vector field into the dual-number ring, our method extracts both the composite barrier value and its exact directional derivative in a single evaluation. The standard floating-point minimum deterministically isolates a single vertex of the Clarke generalized gradient for the quadratic-program solver. We prove this selected vertex constitutes a Clarke subgradient and the resulting simultaneous-enforcement safety filter guarantees forward invariance. The arithmetic overhead remains a fixed constant factor, independent of state dimension and constraint count. We extend this framework to finite $\\min$/$\\max$ Boolean compositions, for which enforcement of the routed constraint of each $δ$-active clause guarantees forward invariance, and to systems of higher relative degree, for which a bivariate truncated-dual evaluation extracts the control coupling without symbolic differentiation. Three numerical examples illustrate the computational scaling.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.25333",
  "author_total": 1,
  "authors": [
    {
      "name": "Mohammadreza Kamaldar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/558zqtwz87btv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.25333",
  "fulltext_url": null,
  "id": "558zqtwz87btv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.25333",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.SY"
    ],
    [
      "arxiv",
      "eess.SY"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Formal Methods in Verification"
    ]
  ],
  "openalex": "W7165934810",
  "pdf_url": "https://arxiv.org/pdf/2606.25333",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/558zqtwz87btv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2606.25333",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.25333"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Deterministic Non-Smooth Safety via Dual-Algebraic Control Barrier Functions",
  "title_text": "Deterministic Non-Smooth Safety via Dual-Algebraic Control Barrier Functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/558zqtwz87btv",
  "venue": "arXiv",
  "versions": []
}