On Baker-Gill-Solovay Oracle Turing Machines and Relativization Barrier

This work analyses the so-called"Relativization Barrier"with respect to the Baker-Gill-Solovay oracle Turing machine. We show that the {\em diagonalization} technique is a valid mathematical proof technique, but it has some prerequisites when referring to the"relativization barrier."

[1]  Tianrong Lin.  Diagonalization of Polynomial-Time Deterministic Turing Machines Via Nondeterministic Turing Machine , 2021, 2110.06211.

[2]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[3]  Sanjeev Arora,et al.  Computational Complexity: A Modern Approach , 2009 .

[4]  Avi Wigderson,et al.  Algebrization: A New Barrier in Complexity Theory , 2009, TOCT.

[5]  A. Wigderson,et al.  Algebrization: a new barrier in complexity theory , 2008, STOC.

[6]  Robert Gray,et al.  Georg Cantor and Transcendental Numbers , 1994 .

[7]  J. Hartmanis,et al.  On the Computational Complexity of Algorithms , 1965 .

[8]  R. Carmichael.  The Theory of Functions of a Real Variable and the Theory of Fourier's Series , 1928, Nature.

[9]  Tianrong Lin.  Diagonalization of Polynomial-Time Turing Machines Via Nondeterministic Turing Machine , 2021, ArXiv.

[10]  Tianrong Lin.  Resolution of The Linear-Bounded Automata Question , 2021, arXiv.org.

[11]  Eric Bach,et al.  Affine Relativization: Unifying the Algebrization and Relativization Barriers , 2016, Electron. Colloquium Comput. Complex..

[12]  Lance Fortnow,et al.  Diagonalization , 2000, Bull. EATCS.

[13]  John Gill,et al.  Relativizations of the P =? NP Question , 1975, SIAM J. Comput..

[14]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[15]  W. Rudin.  Principles of mathematical analysis , 1964 .

[16]  G. H. H.,et al.  The Theory of Functions of a Real Variable and the Theory of Fourier's Series , 1907, Nature.