# Research Publications

**Algorithmic Information Bounds for Distances and Orthogonal Projections**  
Peter Cholak, Marianna Csörnyei, Neil Lutz, Patrick Lutz, Elvira Mayordomo, and D. M. Stull  
Mathematical Foundations of Computer Science (MFCS), 2026  
★ Best Paper Award  
[\[arXiv\]](https://arxiv.org/abs/2509.05211)

**Multi-Head Finite-State Dimension**  
Xiang Huang, Xiaoyuan Li,  Jack H. Lutz, and Neil Lutz  
Mathematical Foundations of Computer Science (MFCS), 2026  
[\[arXiv\]](https://arxiv.org/abs/2509.22912)

**One Adaptive Trailing Head Can Outperform Many Oblivious Trailing Heads**  
Julianne Cruz, Sho Glashausser, and Neil Lutz  
Machines, Computations, and Universality (MCU), 2026  
[\[arXiv\]](https://arxiv.org/abs/2606.00127)

**Adaptive Multi-Head Finite-State Gamblers**  
Julianne Cruz, Sho Glashausser, Xiaoyuan Li, and Neil Lutz  
Computability in Europe (CiE), 2026  
[\[arXiv\]](https://arxiv.org/abs/2603.16034)

**Lines in Every Direction with No ee-Random Points**  
Neil Lutz, Spencer Park Martin, and Rain White  
Computability in Europe (CiE), 2026  
[\[arXiv\]](https://arxiv.org/abs/2507.05475)

**Multi-Head Finite-State Compression**  
Neil Lutz  
Latin American Theoretical Informatics Symposium (LATIN), 2026  
[\[arXiv\]](https://arxiv.org/abs/2510.17544)

**Bounding the Dimension of Exceptional Sets for Orthogonal Projections**  
Peter Cholak, Marianna Csörnyei, Neil Lutz, Patrick Lutz, Elvira Mayordomo, and D. M. Stull  
*Proceedings of the American Mathematical Society*, in press  
[\[arXiv\]](https://arxiv.org/abs/2411.04959)

**Algorithmically Optimal Outer Measures**  
Jack H. Lutz and Neil Lutz  
*ACM Transactions on Computation Theory*, 2025  
[\[arXiv\]](https://arxiv.org/abs/2006.08468) · [\[journal\]](https://dl.acm.org/doi/full/10.1145/3733607)

**Projection Theorems Using Effective Dimension**  
Neil Lutz and D. M. Stull  
Mathematical Foundations of Computer Science (MFCS), 2018  
*Information and Computation*, 2024  
[\[arXiv\]](https://arxiv.org/abs/1711.02124) · [\[conference\]](https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.71) · [\[journal\]](https://www.sciencedirect.com/science/article/pii/S0890540124000026)

**Extending the Reach of the Point-to-Set Principle**  
Jack H. Lutz, Neil Lutz, and Elvira Mayordomo  
Symposium on Theoretical Aspects of Computer Science (STACS), 2022  
*Information and Computation*, 2023  
[\[arXiv\]](https://arxiv.org/abs/2004.07798) · [\[conference\]](https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2022.48) · [\[journal\]](https://www.sciencedirect.com/science/article/pii/S0890540123000810)

**Dimension and the Structure of Complexity Classes**  
Jack H. Lutz, Neil Lutz, and Elvira Mayordomo  
*Theory of Computing Systems* (Commemorative Issue for Alan L. Selman), 2023  
[\[arXiv\]](https://arxiv.org/abs/2109.05956) · [\[journal\]](https://link.springer.com/article/10.1007/s00224-022-10096-7)

**Dimension Spectra of Lines**  
Neil Lutz and D. M. Stull  
Computability in Europe (CiE), 2017  
*Computability*, 2022  
[\[arXiv\]](https://arxiv.org/abs/1701.04108) · [\[conference\]](https://link.springer.com/chapter/10.1007/978-3-319-58741-7_29) · [\[journal\]](https://journals.sagepub.com/doi/abs/10.3233/COM-190292)

**Fractal Intersections and Products via Algorithmic Dimension**  
Neil Lutz  
Mathematical Foundations of Computer Science (MFCS), 2017  
 ★ Best Student Paper Award  
*ACM Transactions on Computation Theory*, 2021  
[\[arXiv\]](https://arxiv.org/abs/1612.01659) · [\[conference\]](https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.58) · [\[journal\]](https://dl.acm.org/doi/abs/10.1145/3460948)

**Bounding the Dimension of Points on a Line**  
Neil Lutz and D. M. Stull  
Theory and Applications of Models of Computation (TAMC), 2017  
*Information and Computation*, 2020  
[\[arXiv\]](https://arxiv.org/abs/1612.00143) · [\[conference\]](https://link.springer.com/chapter/10.1007/978-3-319-55911-7_31) · [\[journal\]](https://www.sciencedirect.com/science/article/pii/S0890540120300894)

**A Center in Your Neighborhood: Fairness in Facility Location**  
Christopher Jung, Sampath Kannan, and Neil Lutz  
Symposium on Foundations of Responsible Computing (FORC), 2020  
[\[arXiv\]](https://arxiv.org/abs/1908.09041) · [\[conference\]](https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2020.5)

**Quantifying the Burden of Exploration and the Unfairness of Free Riding**  
Christopher Jung, Sampath Kannan, and Neil Lutz  
Symposium on Discrete Algorithms (SODA), 2020  
[\[arXiv\]](https://arxiv.org/abs/1810.08743) · [\[conference\]](https://epubs.siam.org/doi/10.1137/1.9781611975994.116)

**Robustness and Games Against Nature in Molecular Programming**  
Jack H. Lutz, Neil Lutz, Robyn R. Lutz, and Matthew R. Riley  
International Conference on Software Engineering: New Ideas and Emerging Results (ICSE-NIER), 2019  
[\[arXiv\]](https://arxiv.org/abs/1902.06171) · [\[conference\]](https://ieeexplore.ieee.org/document/8805682)

**Algorithmic Information, Plane Kakeya Sets, and Conditional Dimension**  
Jack H. Lutz and Neil Lutz  
Symposium on Theoretical Aspects of Computer Science (STACS), 2017  
*ACM Transactions on Computation Theory*, 2018  
[\[arXiv\]](https://arxiv.org/abs/1511.00442) · [\[conference\]](https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.53) · [\[journal\]](https://dl.acm.org/doi/pdf/10.1145/3201783)

**Dynamics at the Boundary of Game Theory and Distributed Computing**  
Aaron D. Jaggard, Neil Lutz, Michael Schapira, and Rebecca N. Wright  
*ACM Transactions on Economics and Computation*, 2017  
[\[arXiv\]](https://arxiv.org/abs/1509.02955) · [\[journal\]](https://dl.acm.org/doi/abs/10.1145/3107182)

**Stateless Computation**  
Danny Dolev, Michael Erdmann, Neil Lutz, Michael Schapira, and Adva Zair  
Brief announcement at ACM Symposium on Principles of Distributed Computing (PODC), 2017  
[\[arXiv\]](https://arxiv.org/abs/1611.10068) · [\[conference\]](https://dl.acm.org/doi/10.1145/3087801.3087854)

**Lines Missing Every Random Point**  
Jack H. Lutz and Neil Lutz  
Computability in Europe (CiE), 2014  
*Computability*, 2015  
[\[arXiv\]](https://arxiv.org/abs/1401.3063) · [\[conference\]](https://link.springer.com/chapter/10.1007/978-3-319-08019-2_29) · [\[journal\]](https://sage.cnpereading.com/doi/10.3233/COM-150038)

**Self-Stabilizing Uncoupled Dynamics**  
Aaron D. Jaggard, Neil Lutz, Michael Schapira, and Rebecca N. Wright  
Symposium on Algorithmic Game Theory (SAGT), 2014  
[\[arXiv\]](https://arxiv.org/abs/1403.5791) · [\[conference\]](https://link.springer.com/chapter/10.1007/978-3-662-44803-8_7)

**Examining the Reuse of Open Textbooks**  
John Levi Hilton III, Neil Lutz, and David Wiley  
The International Review of Research in Open and Distributed Learning, 2012  
[\[journal\]](https://www.irrodl.org/index.php/irrodl/article/view/1137)


# Expository Writing **Who Asked Us? How the Theory of Computing Answers Questions about Analysis** Jack H. Lutz and Neil Lutz *Complexity and Approximation*, Ding-Zhu Du and Jie Wang (eds.), 2020 [\[arXiv\]](https://arxiv.org/abs/1912.00284) · [\[book\]](https://link.springer.com/chapter/10.1007/978-3-030-41672-0_4) **Some Open Problems in Algorithmic Fractal Geometry** Neil Lutz, edited by William Gasarch Open Problems Column, *SIGACT News*, 2017 [\[pdf\]](assets/fracgeom.pdf) · [\[newsletter\]](https://dl.acm.org/doi/abs/10.1145/3173127.3173134)
# Preprints **Algorithmic Randomness in Continuous-Time Markov Chains** Xiang Huang, Jack H. Lutz, Neil Lutz, and Andrei Migunov [\[arXiv\]](https://arxiv.org/abs/1910.13620)