|
| This Article | ||
| | ||
| Share | ||
| Bibliographic References | ||
| Add to: | ||
 Digg  Furl  Spurl  Blink  Simpy  Google  Del.icio.us  Y!MyWeb | ||
| Search | ||
| ||
35th Annual Symposium on Foundations of Computer Science (FOCS 1994)
The complexity of the membership problem for 2-generated commutative semigroups of rational matrices (PDF)
Santa Fe, NM, USA
November 20-November 22
ISBN: 0-8186-6580-7
| ASCII Text | x | ||
| Jin-yi Cai, R.J. Lipton, Y. Zalcstein, "The complexity of the membership problem for 2-generated commutative semigroups of rational matrices," Foundations of Computer Science, IEEE Annual Symposium on, pp. 135-142, 35th Annual Symposium on Foundations of Computer Science (FOCS 1994), 1994. | |||
| BibTex | x | ||
| @article{ 10.1109/SFCS.1994.365699, author = { Jin-yi Cai and R.J. Lipton and Y. Zalcstein}, title = {The complexity of the membership problem for 2-generated commutative semigroups of rational matrices}, journal ={Foundations of Computer Science, IEEE Annual Symposium on}, volume = {0}, year = {1994}, isbn = {0-8186-6580-7}, pages = {135-142}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.1994.365699}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - CONF JO - Foundations of Computer Science, IEEE Annual Symposium on TI - The complexity of the membership problem for 2-generated commutative semigroups of rational matrices SN - 0-8186-6580-7 SP135 EP142 A1 - Jin-yi Cai, A1 - R.J. Lipton, A1 - Y. Zalcstein, PY - 1994 KW - polynomial-sized encoding KW - membership problem complexity KW - 2-generated commutative semigroups KW - rational matrices KW - deterministic polynomial-time algorithm KW - ABC problem KW - algebraic number field KW - polynomial time algorithm KW - 2-generated abelian linear groups VL - 0 JA - Foundations of Computer Science, IEEE Annual Symposium on ER - | |||
We present a deterministic polynomial-time algorithm for the ABC problem, which is the membership problem for 2-generated commutative linear semigroups over an algebraic number field. We also obtain a polynomial time algorithm, for the (easier) membership problem, for 2-generated abelian linear groups. Furthermore, we provide a polynomial-sized encoding for the set of all solutions.
Index Terms:
polynomial-sized encoding, membership problem complexity, 2-generated commutative semigroups, rational matrices, deterministic polynomial-time algorithm, ABC problem, algebraic number field, polynomial time algorithm, 2-generated abelian linear groups
Citation:
Jin-yi Cai, R.J. Lipton, Y. Zalcstein, "The complexity of the membership problem for 2-generated commutative semigroups of rational matrices," focs, pp.135-142, 35th Annual Symposium on Foundations of Computer Science (FOCS 1994), 1994
Usage of this product signifies your acceptance of the Terms of Use.