Shmuel Friedland - University of Illinois at Chicago It is known that the complexity of computing the rank of d-tensor and its best rank one approximation is NP-hard over the complex numbers for d 3. But what are the known upper bounds for the bit complexity of these quantities for general and symmetric tensors? We claim that these problems are hard to compute because they are intimately related to solubility of system of polynomial equations. We first will discuss the recent results in [2] which shows that if we fix the dimension n of a symmetric d-tensor then the bit complexity of computation of best rank one symmetric approximation of a symmetric tensor is of at most of order O(d8n). For qubits (n=2) the bit complexity is O(d8). We second discuss how to convert the problem of finding whether a rank of a given d-tensor is at most r equivalent to a nonsolubility of a system of linear equations with many variables. The upper bound on complexity is O(d3d2r4). References [1] M. Aliabadi and S. Friedland, On the complexity of finding tensor ranks, to appear in Communications on Applied Mathematics and Computation, arXiv:2002.07151. [2] S. Friedland and L. Wang, Spectral norm of a symmetric tensor and its computation, Mathematics of Computation, 89 (2020)., 2175-2215.