# 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…

## 4 Citations

Refuting Tianrong Lin's arXiv: 2110.05942 "Resolution of The Linear-Bounded Automata Question"

- MathematicsArXiv
- 2021

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

- Computer ScienceArXiv
- 2021

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

- BusinessArXiv
- 2021

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

- Computer Science
- 2021

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.

## References

SHOWING 1-10 OF 31 REFERENCES

Diagonalization of Polynomial-Time Turing Machines Via Nondeterministic Turing Machine

- Computer ScienceArXiv
- 2021

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 .

Relationships Between Nondeterministic and Deterministic Tape Complexities

- Computer ScienceJ. Comput. Syst. Sci.
- 1970

Some Results on Tape-Bounded Turing Machines

- Computer ScienceJACM
- 1969

It is shown that the lower bounds on tape complexity of [1] depend on neither the halting assumption nor determinism, and that below log n tape complexity there exists a dense hierarchy of complexity classes for two-way nondeterministic devices.

The method of forced enumeration for nondeterministic automata

- Computer ScienceActa Informatica
- 2004

SummaryEvery family of languages, recognized by nondeterministic L(n) tape-bounded Turing machines, where L(n)≥logn, is closed under complement. As a special case, the family of context-sensitive…

Formal languages and their relation to automata

- Computer ScienceAddison-Wesley series in computer science and information processing
- 1969

The theory of formal languages as a coherent theory is presented and its relationship to automata theory is made explicit, including the Turing machine and certain advanced topics in language theory.

Nondeterministic space is closed under complementation

- Mathematics[1988] Proceedings. Structure in Complexity Theory Third Annual Conference
- 1988

It is shown that nondeterministic space s(n) is closed under complementation for s(n) greater than or equal to log n. It immediately follows that the context-sensitive languages are closed under…

Introduction to the Theory of Computation

- Philosophy
- 2018

Exercise 1. A 2-counter machine (2CM) has a finite state control, and two stacks on which it can push and pop tokens, where these tokens are all alike. The transition function for a 2CM takes as…

On Computable Numbers, with an Application to the Entscheidungsproblem

- Computer Science
- 1937

This chapter discusses the application of the diagonal process of the universal computing machine, which automates the calculation of circle and circle-free numbers.