The Complexity of the A B C Problem

Authors:
Jin-yi Cai;Richard J. Lipton;Yechezkel Zalcstein
Affiliations:
-;-;-
Venue:
SIAM Journal on Computing
Year:
2000

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The orbit problem in higher dimensions

Proceedings of the forty-fifth annual ACM symposium on Theory of computing

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Abstract

We present a deterministic polynomial-time algorithm for the A B C 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.