This work resolve a longstanding open question in automata theory, i.e. the {\it linear-bounded automata question} ( shortly, {\it LBA question}), which can also be phrased succinctly in the language of computational complexity theory as $NSPACE[n]\overset{?}{=}DSPACE[n]$. We prove that $NSPACE[n]\neq DSPACE[n]$. Our proof technique is based on diagonalization against all deterministic Turing machines working in $O(n)$ space by an universal nondeterministic Turing machine running in $O(n)$ space. Our proof also implies the following consequences: (1) There exists no deterministic Turing machine working in $O(\log n)$ space deciding the $st$-connectivity question (STCON); (2) $L\neq NL$; (3) $L\neq P$.

翻译：这项工作解决了自动化理论中一个长期未决问题,即 ~ ~ ~ 线性自成一体的自成一体的自成一体的自成一体的自成一体的自成一体的质问 } ( ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ $ 。 我们证明$ NSPACE\\ n. DESPACE $. 。 我们的验证技术基于对在 $O (n) 的范围内工作的所有确定性图灵机器的二分法化,由在$O (n) 空间运行的通用非确定性图灵机进行。 我们的证据还暗示了以下后果:(1) 在 $O (\ log n ) 上没有确定性图灵机在决定 $st$ 连接问题的空间上工作 ; (2) $L\ Q NL ; (3) $L\ Q P$ 。