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：针对系数为可计算序列的线性差分方程，我们建立了确定其解空间维数问题的算法不可判定性，该结论在已知解空间维数部分先验信息的情况下依然成立。