Resolution of the LinearBounded Automata Question
Abstract
This work resolve a longstanding open question in automata theory, i.e. the {\it linearbounded 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) $L\neq P$.
 Publication:

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.05942
 Bibcode:
 2021arXiv211005942L
 Keywords:

 Computer Science  Computational Complexity;
 Computer Science  Formal Languages and Automata Theory;
 F.1.1;
 F.1.3
 EPrint:
 The definition of enumeration supplemented, feedbacks are welcome. arXiv admin note: text overlap with arXiv:2106.11886