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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1305.5617 |
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| _version_ | 1866909178449100800 |
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| author | Niemeyer, Alice C. Popiel, Tomasz Praeger, Cheryl E. Rademacher, Daniel |
| author_facet | Niemeyer, Alice C. Popiel, Tomasz Praeger, Cheryl E. Rademacher, Daniel |
| contents | We suggest that straight-line programs designed for algebraic computations should be accompanied by a comprehensive complexity analysis that takes into account both the number of fundamental algebraic operations needed, as well as memory requirements arising during evaluation. We introduce an approach for formalising this idea and, as illustration, construct and analyse straight-line programs for the Bruhat decomposition of $d\times d$ matrices with determinant $1$ over a finite field of order $q$ that have length $O(d^2\log(q))$ and require storing only $O(\log(q))$ matrices during evaluation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1305_5617 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Showcasing straight-line programs with memory via matrix Bruhat decomposition Niemeyer, Alice C. Popiel, Tomasz Praeger, Cheryl E. Rademacher, Daniel Data Structures and Algorithms Group Theory We suggest that straight-line programs designed for algebraic computations should be accompanied by a comprehensive complexity analysis that takes into account both the number of fundamental algebraic operations needed, as well as memory requirements arising during evaluation. We introduce an approach for formalising this idea and, as illustration, construct and analyse straight-line programs for the Bruhat decomposition of $d\times d$ matrices with determinant $1$ over a finite field of order $q$ that have length $O(d^2\log(q))$ and require storing only $O(\log(q))$ matrices during evaluation. |
| title | Showcasing straight-line programs with memory via matrix Bruhat decomposition |
| topic | Data Structures and Algorithms Group Theory |
| url | https://arxiv.org/abs/1305.5617 |