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George Kenison

Research Summary

Brief Overview
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George’s research addresses open problems concerning loop programs, (semi)groups, iterative maps, and recurrence sequences. His work designs and analyses algorithms to better understand the limits of computation: sharpening the known boundaries between decidability and undecidability. He is particularly interested in connections with dynamical systems, abstract algebra, and formal languages. Much of this work is motivated by the mathematics underpinning different models of computation as well as applications in program analysis and verification. Recent projects include work on decision procedures concerning the orbits of linear dynamical systems and loop programs; generating and verifying polynomial invariants for infinite-state systems; and synthesising loop programs from algebraic specifications.

Peer-reviewed papers in conference proceedings
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  • On Word Representations and Embeddings in Complex Matrices. DOI đź”— (with Paul C. Bell, Reino Niskanen, Igor Potapov, and Pavel Semukhin). In: Proceedings of the International Conference on Developments in Language Theory, DLT 2026.

  • The Threshold Problem for Hypergeometric Sequences with Quadratic Parameters. DOI đź”— In: 51st International Colloquium on Automata, Languages, and Programming, ICALP 2024.

  • Linear Loop Synthesis for Quadratic Invariants DOI đź”— (with S. Hitarth, Laura Kovács, and Anton Varonka). In: 41st International Symposium on Theoretical Aspects of Computer Science, STACS 2024.

  • From Polynomial Invariants to Linear Loops. DOI đź”— (with Laura Kovács and Anton Varonka). In: Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 2023.

  • The Membership Problem for Hypergeometric Sequences with Quadratic Parameters. DOI đź”— (with Klara Nosan, Mahsa Shirmohammadi, and James Worrell). In: Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 2023.

  • Positivity Problems for Reversible Linear Recurrence Sequences. DOI đź”— (with Joris Nieuwveld, JoĂ«l Ouaknine, and James Worrell). In: 50th International Colloquium on Automata, Languages, and Programming, ICALP 2023.

  • On the Skolem Problem for Reversible Sequences DOI đź”— In: International Symposium on Mathematical Foundations of Computer Science, MFCS 2022.

  • Solving Invariant Generation for Unsolvable Loops. DOI đź”— (with Daneshvar Amrollahi, Ezio Bartocci, Laura Kovács, Marcel Moosbrugger, and Miroslav StankoviÄŤ). In Static Analysis: 29th International Symposium, SAS 2022.

  • On Positivity and Minimality for Second-Order Holonomic Sequences. DOI đź”— (with Oleksiy Klurman, Engel Lefaucheux, Florian Luca, Pieter Moree, JoĂ«l Ouaknine, Markus A. Whiteland, and James Worrell). In: International Symposium on Mathematical Foundations of Computer Science, MFCS 2021.

  • On the Skolem Problem and Prime Powers. DOI đź”— (with Richard Lipton, JoĂ«l Ouaknine, and James Worrell). In: Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC 2020.

Peer-reviewed articles in journals
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  • Determination Problems for Orbit Closures and Matrix Groups. DOI đź”— (with Rida Ait El Manssour, Mahsa Shirmohammadi, Anton Varonka, and James Worrell). In: Proc. ACM Program. Lang., 10 POPL, pp. 1615–1640.

  • Simple Linear Loops: Algebraic Invariants and Applications. DOI đź”— (with Rida Ait El Manssour, Mahsa Shirmohammadi, and Anton Varonka). In: Proc. ACM Program. Lang., 9 POPL, pp. 745–771.

  • (Un)Solvable loop analysis. DOI đź”— (with Daneshvar Amrollahi, Ezio Bartocci, Laura Kovács, Marcel Moosbrugger, and Miroslav StankoviÄŤ). In: Formal Methods in System Design, 2024.

  • Statistics in conjugacy classes in free groups. DOI đź”— (with Richard Sharp). In: Geometriae Dedicata 198.1, pp. 57–70.

  • Orbit counting in conjugacy classes for free groups acting on trees. DOI đź”— (with Richard Sharp). In: Journal of Topology and Analysis 9.4, pp. 631–647.

Preprints
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  • On the Positivity Problem for second-order holonomic sequences. (with Oleksiy Klurman, Engel Lefaucheux, Florian Luca, Pieter Moree, JoĂ«l Ouaknine, Emre Sertöz, Markus A. Whiteland, and James Worrell).

  • On the growth of hypergeometric sequences. arXiv đź”— (with Jakub Konieczny, Florian Luca, Andrew Scoones, Mahsa Shirmohammadi, and James Worrell).