# Determinant versus permanent

```@inproceedings{Agrawal2006DeterminantVP,
title={Determinant versus permanent},
author={Manindra Agrawal},
year={2006}
}```
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…

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