• Corpus ID: 238634280

Resolution of The Linear-Bounded Automata Question

  title={Resolution of The Linear-Bounded Automata Question},
  author={Tianrong Lin},
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"
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
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
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
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.


Relationships Between Nondeterministic and Deterministic Tape Complexities
  • W. Savitch
  • Computer Science, Mathematics
    J. Comput. Syst. Sci.
  • 1970
The amount of storage needed to simulate a nondeterministic tape bounded Turingmachine on a deterministic Turing machine is investigated and a specific set is produced, namely the set of all codings of threadable mazes, such that, if there is any set which distinguishes nondeter microscopic complexity classes from deterministic tape complexity classes, then this is one such set.
Some Results on Tape-Bounded Turing Machines
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
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
  • J. Hopcroft, J. Ullman
  • Computer Science
    Addison-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.
Introduction to Automata Theory, Languages and Computation
This book is a rigorous exposition of formal languages and models of computation, with an introduction to computational complexity, appropriate for upper-level computer science undergraduates who are comfortable with mathematical arguments.
Introduction to the Theory of Computation
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
A Survey of Space Complexity
  • Pascal Michel
  • Computer Science, Mathematics
    Theor. Comput. Sci.
  • 1992
The space complexity of RAMs is defined and its relation to usual classes is given, and three ways of relativizing complexity classes are examined.
On Computable Numbers, with an Application to the Entscheidungsproblem
1. Computing machines. 2. Definitions. Automatic machines. Computing machines. Circle and circle-free numbers. Computable sequences and numbers. 3. Examples of computing machines. 4. Abbreviated
Undirected connectivity in log-space
A deterministic, log-space algorithm that solves st-connectivity in undirected graphs and implies a way to construct in log- space a fixed sequence of directions that guides a deterministic walk through all of the vertices of any connected graph.
Hierarchies of memory limited computations
This paper investigates the computational complexity of binary sequences as measured by the rapidity of their generation by multitape Turing machines. A "translational" method which escapes some of