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Linear automaton transformations
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“The classic Myhill-Nerode theorem [26, 27] provides intuition: every pair of distinct states can be distinguished by some sequence (admitted by one state but not the other). Unless those minimal distinguishing sequences are of length one, looking at the next single token outputted will not reliably assess whether the generative model has an accurate model of the underlying state.”
From Evaluating the World Model Implicit in a Generative Model (2024) · cites this paper as [27]
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“The Myhill-Nerode theorem states that the sets of sequences accepted by a minimal DFA starting at two distinct states are distinct (see Appendix C for a full statement).”
From Evaluating the World Model Implicit in a Generative Model (2024) · cites this paper as [27]
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Subspace-based signal analysis using singular value decomposition
Van Der Veen, A.-J., Deprettere, E. F., & Swindlehurst, A. L. (1993) · Proceedings of the IEEE · doi:10.1109/5.237536 · Cited by 348
Approximate information state for partially observed systems
Subramanian, J., & Mahajan, A. (2019) · 2019 IEEE 58th Conference on Decision and Control (CDC) · doi:10.1109/cdc40024.2019.9029898 · Cited by 23
Evaluating the World Model Implicit in a Generative Model
Vafa, K., Chen, J., Rambachan, A., Kleinberg, J., & Mullainathan, S. (2024) · Advances in Neural Information Processing Systems 37 · doi:10.52202/079017-0846 · Cited by 22
Metadata
- Authors
- Nerode, A.
- Corresponding author
- Nerode, A.
- Venue
- Proceedings of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Published
- 1958-08
- Volume
- 9
- Issue
- 4
- Pages
- 541-544
- ISSN
- 0002-9939 (ISSN-L)
- 1088-6826
- OpenAlex
- W2088432971
- Cited by
- 541
- References
- 0
- Citations by year
- 2026: 14 · 2025: 19 · 2024: 10 · 2023: 17 · 2022: 23 · 2021: 22 · 2020: 18 · 2019: 19 · 2018: 18 · 2017: 14 · 2016: 16 · 2015: 27 · 2014: 25 · 2013: 14 · 2012: 17
- FWCI
- 4.61
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Proceedings of the American Mathematical Society (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › semigroups and automata theory
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Cellular Automata and Applications
- Keywords
- linear automata, automata theory, linear operators
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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Cite CoChat for the checks on this page, and the paper for its own findings.
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- CoChat. (2026). Citation check: Linear automaton transformations. https://app.cochat.ai/papers/10.1090/s0002-9939-1958-0135681-9
- The paper
- Nerode, A. (1958). Linear automaton transformations. Proceedings of the American Mathematical Society. https://doi.org/10.1090/s0002-9939-1958-0135681-9
