• Corpus ID: 238634280

Resolution of The Linear-Bounded Automata Question

@article{Lin2021ResolutionOT,
  title={Resolution of The Linear-Bounded Automata Question},
  author={Tianrong Lin},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.05942}
}
This work resolve a longstanding open question in automata theory, i.e. the linear-bounded automata question ( shortly, LBA question), which can also be phrased succinctly in the language of computational complexity theory as NSPACE[n] ? = DSPACE[n]. We prove that NSPACE[n] 6= DSPACE[n]. Our proof technique is based on diagonalization against all deterministic Turing machines working in O(n) space. Our proof also implies the following consequences: (1) There exists no deterministic Turing… 
Refuting Tianrong Lin's arXiv: 2110.05942 "Resolution of The Linear-Bounded Automata Question"
TLDR
It is demonstrated that Mr. Tianrong's proof is incomplete, even wrong, and his strategy cannot be repaired, so his claim to prove NSPACE[n] 6= DSPACE(n) for suitable S(n).
Diagonalization of Polynomial-Time Turing Machines Via Nondeterministic Turing Machine
TLDR
It is obtained that there is a language Ld not accepted by any polynomial-time deterministic Turing machines but accepted by a nondeterministic Turing machine working within O(nk) for any k ∈ N1, i.e. Ld ∈ NP .
On Baker-Gill-Solovay Oracle Turing Machines and Relativization Barrier
TLDR
It is shown that the diagonalization technique is a valid mathematical proof technique, but it has some prerequisites when referring to “Relativization barrier”.
Diagonalizing Against Polynomial-Time Bounded Turing Machines Via Nondeterministic Turing Machine
TLDR
This work enumerates all polynomial-time deterministic Turing machines and diagonalize over all of them by an universal nondeterministic Turing machine, and obtains a proof that P and NP differs.

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