Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resolution of the Linear-Bounded Automata Question   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) $L\neq P$.

15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin