Submitted Publications

• Clemens Hofstadler, Clemens G. Raab, and Georg Regensburger. Universal truth of operator statements via ideal membership. Submitted, 33 pages, 2022. arXiv

Refereed Publications

• Clemens Hofstadler and Thibaut Verron. Short proofs of ideal membership. Journal of Symbolic Computation 125, 102325, 23 pages, 2024. DOI | arXiv
• Klara Bernauer, Clemens Hofstadler, and Georg Regensburger. How to Automatise Proofs of Operator Statements: Moore-Penrose Inverse – A Case Study. Proceedings of CASC 2023, p. 39–68, 2023. DOI | arXiv
• Clemens Hofstadler and Thibaut Verron. Signature Gröbner bases in free algebras over rings. Proceedings of ISSAC 2023, p. 298–306, 2023. DOI | arXiv
• 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
• Clemens Hofstadler and Thibaut Verron. Signature Gröbner bases, bases of syzygies and cofactor reconstruction in the free algebra. Journal of Symbolic Computation 113, p. 211–241, 2022. DOI | arXiv
• 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
• Cyrille Chenavier, Clemens Hofstadler, Clemens G. Raab, and Georg Regensburger. Compatible rewriting of noncommutative polynomials for proving operator identities. Proceedings of ISSAC 2020, p. 83–90, 2020. DOI | arXiv
• Clemens Hofstadler, Clemens G. Raab, and Georg Regensburger. Certifying operator identities via noncommutative Gröbner bases. ACM Communications in Computer Algebra 53, 2, p. 49–52, 2019. DOI

Other Publications

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

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