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The bounded membership problem of the monoidSL 2(N)

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Abstract

SL 2(N) is the set of all 2 × 2 matrices with nonnegative integer entries and determinant 1. The bounded membership problem (BMN) ofSL 2(N) is that given a subsetS ofSL 2(N), a matrixA εSL 2(N), and an integern, whetherA can be represented as a product of at mostn matrices (repetitions are allowed) inS. We prove that BMN is NP-complete, but its randomized version under natural distribution is solvable in average polynomial time. Furthermore, it is proved that if the number of elements ofS is a constant, then BMN is polynomial time computable.

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Authors and Affiliations

  1. Department of Computer Science, State University of New York at Buffalo, 14260, Buffalo, NY, USA

    J. Cai

  2. Department of Computer Science, Princeton University, 08544, Princeton, NJ, USA

    Z. Liu

Authors
  1. J. Cai
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  2. Z. Liu
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Additional information

J. Cai was supported in part by NSF Grants CCR 9057486 and CCR 9319093, and an Alfred P. Sloan Fellowship. Z. Liu was supported in part by NSF Grant CCR 9057486.

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Cai, J., Liu, Z. The bounded membership problem of the monoidSL 2(N). Math. Systems Theory 29, 573–587 (1996). https://doi.org/10.1007/BF01301965

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  • DOI: https://doi.org/10.1007/BF01301965

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