Decidability of the membership problem for 2 x 2 integer matrices
- Submitting institution
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University of Oxford
- Unit of assessment
- 11 - Computer Science and Informatics
- Output identifier
- 12098
- Type
- E - Conference contribution
- DOI
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10.1137/1.9781611974782.12
- Title of conference / published proceedings
- SODA '17 Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
- First page
- 170
- Volume
- -
- Issue
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- ISSN
- -
- Open access status
- -
- Month of publication
- January
- Year of publication
- 2017
- URL
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- Supplementary information
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- Request cross-referral to
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- Output has been delayed by COVID-19
- No
- COVID-19 affected output statement
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- Forensic science
- No
- Criminology
- No
- Interdisciplinary
- No
- Number of additional authors
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1
- Research group(s)
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-
- Citation count
- 7
- Proposed double-weighted
- No
- Reserve for an output with double weighting
- No
- Additional information
- This paper proposes an algorithm for the following problem: given 2x2 nonsingular integer matrices M1,...,Mn and M, decide whether M belongs to the semigroup generated by M1,...,Mn. Semigroups of 2x2 matrices are not only fundamental in geometry, topology, and representation theory, but are a natural decidability borderline for the membership problem. This is the first significant breakthrough on this topic since 2005, when decidability was shown for matrices with determinants 1,-1. Hrushovski et al., LICS’18 (https://doi.org/10.1145/3209108.3209142), acknowledge its importance, and our approach to the problem is included among future lines of research by Ouaknine et al. in JACM’19 (https://doi.org/10.1145/3286487).
- Author contribution statement
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- Non-English
- No
- English abstract
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