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THE COMPLEXITY OF THE A BC PROBLEM.

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Title: THE COMPLEXITY OF THE A BC PROBLEM.
Authors: Jin-Yi Cai1 cai@cs.buffalo.edu, Lipton, Richard J.2 rjl@cs.princeton.edu, Yechezkel Zalcstein3 zzalcste@nsf.gov
Source: SIAM Journal on Computing. 2000, Vol. 29 Issue 6, p1878. 11p.
Subjects: Algorithms, Polynomials, Semigroups (Algebra), Group theory
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. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: THE COMPLEXITY OF THE A BC PROBLEM.
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  Data: <searchLink fieldCode="AR" term="%22Jin-Yi+Cai%22">Jin-Yi Cai</searchLink><relatesTo>1</relatesTo><i> cai@cs.buffalo.edu</i><br /><searchLink fieldCode="AR" term="%22Lipton%2C+Richard+J%2E%22">Lipton, Richard J.</searchLink><relatesTo>2</relatesTo><i> rjl@cs.princeton.edu</i><br /><searchLink fieldCode="AR" term="%22Yechezkel+Zalcstein%22">Yechezkel Zalcstein</searchLink><relatesTo>3</relatesTo><i> zzalcste@nsf.gov</i>
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  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Computing%22">SIAM Journal on Computing</searchLink>. 2000, Vol. 29 Issue 6, p1878. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Semigroups+%28Algebra%29%22">Semigroups (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Group+theory%22">Group theory</searchLink>
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  Data: 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. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of SIAM Journal on Computing is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1137/S0097539794276853
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      – SubjectFull: Semigroups (Algebra)
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      – TitleFull: THE COMPLEXITY OF THE A BC PROBLEM.
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              Text: 2000
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