For a linear difference equation with the coefficients being computable sequences, we establish algorithmic undecidability of the problem of determining the dimension of the solution space including the case when some additional prior information on the dimension is available.

翻译：对于系数为可计算序列的线性差分方程，我们确立了判定解空间维数问题的算法不可判定性，包括当维数存在某些额外先验信息的情况。