## The complexity of the membership problem for 2-generated commutative semigroups of rational matrices

Proceedings 35th Annual Symposium on Foundations of Computer Science (1994)

Santa Fe, NM, USA

Nov. 20, 1994 to Nov. 22, 1994

ISBN: 0-8186-6580-7

pp: 135-142

Jin-yi Cai , Dept. of Comput. Sci., State Univ. of New York, Buffalo, NY, USA

ABSTRACT

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

R. Lipton, Jin-yi Cai and Y. Zalcstein, "The complexity of the membership problem for 2-generated commutative semigroups of rational matrices,"

*Proceedings 35th Annual Symposium on Foundations of Computer Science(FOCS)*, Santa Fe, NM, USA, 1994, pp. 135-142.

doi:10.1109/SFCS.1994.365699

CITATIONS