Determinant Versus Permanent
نویسنده
چکیده
We study the problem of expressing permanents of matrices as determinants of (possibly larger) matrices. This problem has close connections to the complexity of arithmetic computations: the complexities of computing permanent and determinant roughly correspond to arithmetic versions of the classes NP and P respectively. We survey known results about their relative complexity and describe two recently developed approaches that might lead to a proof of the conjecture that the permanent can only be expressed as the determinant of exponential-sized matrices. Mathematics Subject Classification (2000). Primary 68Q17; Secondary 68W30.
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Generalized matrix functions, determinant and permanent
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