Publications

Preprints

  1. Clemens Hofstadler and Viktor Levandovskyy. Modular Algorithms For Computing Gröbner Bases in Free Algebras. Submitted, 27 pages, 2025. arXiv
  2. Clemens Hofstadler, Manuel Kauers, and Martina Seidl. Symmetries of Dependency Quantified Boolean Formulas. Submitted, 32 pages, 2024. arXiv
  3. Clemens Hofstadler, Clemens G. Raab, and Georg Regensburger. Universal truth of operator statements via ideal membership. Submitted, 50 pages, 2024. arXiv

Reviewed Publications

  1. Paul Seip, Johannes Fürnkranz, Florian Beck, Clemens Hofstadler, Peter Pfeiffer, Martina Seidl, Robert Peharz, and Stefan Szeider. Towards SAT-Based Learning of NNF Networks. In Proc. of International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC) 2025, to appear. pdf
  2. Daniela Kaufmann and Clemens Hofstadler. Recycling Algebraic Proof Certificates. In Proc. of International Workshop on Satisfiability Checking and Symbolic Computation 2025, vol 4116, pp. 35-40, 2025. URL | arXiv
  3. Maximilian Heisinger and Clemens Hofstadler. f4ncgb: High Performance Gröbner Basis Computations in Free Algebras. In Proc. of International Workshop on Computer Algebra in Scientific Computing (CASC) 2025, Lecture Notes in Computer Science, vol 16235, pp. 79–97, 2025. DOI | arXiv
  4. Andreas Plank, Clemens Hofstadler, Maximilian Heisinger, and Martina Seidl. Refinement-Based Enumeration of QBF Solutions. In Proc. of 19th European Conference on Logics in Artificial Intelligence (JELIA) Part II, pp. 166–181, 2025. DOI | pdf
  5. Clemens Hofstadler and Daniela Kaufmann. Guess and Prove: A Hybrid Approach to Linear Polynomial Recovery in Circuit Verification. In Proc. of 31st Intl. Conference on Principles and Practice of Constraint Programming (CP), pp. 14:1-14:22, 2025. DOI | pdf
  6. Clemens Hofstadler and Thibaut Verron. Short proofs of ideal membership. Journal of Symbolic Computation 125, 102325, 23 pages, 2024. DOI | arXiv
  7. Klara Bernauer, Clemens Hofstadler, and Georg Regensburger. How to Automatise Proofs of Operator Statements: Moore-Penrose Inverse – A Case Study. In Proc. of International Workshop on Computer Algebra in Scientific Computing (CASC) 2023, pp. 39–68, 2023. DOI | arXiv
  8. Clemens Hofstadler and Thibaut Verron. Signature Gröbner bases in free algebras over rings. In Proc. of International Symposium on Symbolic and Algebraic Computation (ISSAC) 2023, pp. 298–306, 2023. DOI | arXiv
  9. Clemens Hofstadler, Clemens G. Raab, and Georg Regensburger. Computing elements of certain form in ideals to prove properties of operators. Mathematics in Computer Science 16, 26 pages, 2022. DOI | arXiv
  10. Clemens Hofstadler and Thibaut Verron. Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebra. Journal of Symbolic Computation 113, pp. 211–241, 2022. DOI | arXiv
  11. Dragana S. Cvetković-Ilić, Clemens Hofstadler, Jamal Hossein Poor, Jovana Milošević, Clemens G. Raab, and Georg Regensburger. Algebraic proof methods for identities of matrices and operators: Improvements of Hartwig’s triple reverse order law. Applied Mathematics and Computation 409, 126357, 10 pages, 2021. DOI | arXiv
  12. Cyrille Chenavier, Clemens Hofstadler, Clemens G. Raab, and Georg Regensburger. Compatible rewriting of noncommutative polynomials for proving operator identities. Proc. of International Symposium on Symbolic and Algebraic Computation (ISSAC) 2020, pp. 83–90, 2020. DOI | arXiv
  13. Clemens Hofstadler, Clemens G. Raab, and Georg Regensburger. Certifying operator identities via noncommutative Gröbner bases. ACM Communications in Computer Algebra 53, 2, pp. 49–52, 2019. DOI

Other Publications

  1. Clemens Hofstadler. Proving Operator Identities with Computer Algebra. Computeralgebra Rundbrief, Ausgabe 74, 2024. pdf

Theses

  • Clemens Hofstadler. Noncommutative Gröbner bases and automated proofs of operator statements. PhD thesis. Johannes Kepler University Linz, Austria, 2023. pdf
  • Clemens Hofstadler. Solving QBFs with AlphaZero and MCTS. Master’s thesis. Johannes Kepler University Linz, Austria, 2022. PURL | pdf
  • Clemens Hofstadler. Certifying operator identities and ideal membership of noncommutative polynomials. Master’s thesis. Johannes Kepler University Linz, Austria, 2020. PURL | pdf