We present new results on the computational limitations of affine automata (AfAs). First, we show that using the endmarker does not increase the computational power of AfAs. Second, we show that the computation of bounded-error rational-valued AfAs can be simulated in logarithmic space. Third, we identify some logspace unary languages that are not recognized by algebraic-valued AfAs. Fourth, we show that using arbitrary real-valued transition matrices and state vectors does not increase the computational power of AfAs in the unbounded-error model. When focusing only the rational values, we obtain the the same result also for bounded error. As a consequence, we show that the class of bounded-error affine languages remains the same when the AfAs are restricted to use rational numbers only.

我们提出仿射自动机（AfAs）的计算限制的新结果。首先，我们表明使用结束标记不会增加AfA的计算能力。其次，我们表明可以在对数空间中模拟有限误差有理值AfA的计算。第三，我们确定一些代数值AfA无法识别的logspace一元语言。第四，我们证明了使用任意实值转换矩阵和状态向量不会增加AfA在无边界误差模型中的计算能力。当仅关注有理值时，对于有界误差，我们也获得相同的结果。结果，我们证明了当AfA仅限于使用有理数时，有界错误仿射语言的类别保持不变。