Conference item
Decidability of the membership problem for 2 x 2 integer matrices
- Abstract:
- The main result of this paper is the decidability of the membership problem for 2 × 2 nonsingular integer matrices. Namely, we will construct the first algorithm that for any nonsingular 2 × 2 integer matrices M1 : : : Mn and M decides whether M belongs to the semigroup generated by fM1 : : : Mng. Our algorithm relies on a translation of nu- merical problems on matrices into combinatorial problems on words. It also makes use of some algebraic properties of well-known subgroups of GL(2; Z) and various new techniques and constructions that help to convert matrix equations into the emptiness problem for intersection of regular languages.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Authors
- Publisher:
- ACM
- Host title:
- SODA '17 Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms
- Journal:
- Proceedings of the Twenty-Eighth Annual ACM-SIAM Symposium on Discrete Algorithms More from this journal
- Pages:
- 170-186
- Series:
- 28th Annual ACM-SIAM Symposium on Discrete Algorithms
- Publication date:
- 2017-01-01
- Acceptance date:
- 2016-10-05
- Event location:
- Barcelona, Spain
- ISBN:
- 9781611974782
- Pubs id:
-
pubs:834451
- UUID:
-
uuid:3fc02e4a-9c58-4d0d-b167-50ae0f1d438a
- Local pid:
-
pubs:834451
- Source identifiers:
-
834451
- Deposit date:
-
2018-09-06
Terms of use
- Copyright holder:
- SIAM
- Copyright date:
- 2017
- Notes:
- Copyright © by SIAM. This is the accepted manuscript version of the article. The final version is available online from ACM at: http://dl.acm.org/citation.cfm?id=3039686.3039698
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