For time, the gold standard for languages with \geq n to read input is \text{TIME}\left(n\right) or at best \text{TIME}\left(n^{k}\right). For space, the gold standard for languages with \geq n characters is \text{SPACE}\left(\log n\right), because to have pointers, store things, etc., will take this much. additional information example Here are some logspace algorithms. 0 and 1 \begin{equation} A = \left{0^{m}1^{m}: m \in \mathbb{N}\right} \end{equation} palendromes We can solve it by keeping track of length of input, and then check x [i] = x[n-i+1]