DeepAI AI Chat
Log In Sign Up

Inquiry of P-reduction in Cook's 1971 Paper – from Oracle machine to Turing machine

by   JianMing Zhou, et al.
Laboratoire des Glucides

In this paper, we inquire the key concept P-reduction in Cook's theorem and reveal that there exists the fallacy of definition in P-reduction caused by the disguised displacement of NDTM from Oracle machine to Turing machine. The definition or derivation of P-reduction is essentially equivalent to Turing's computability. Whether NP problems might been reduced to logical forms (tautology or SAT) or NP problems might been reduced each other, they have not been really proven in Cook's 1971 paper.


Interpretation of NDTM in the definition of NP

In this paper, we interpret NDTM (NonDeterministic Turing Machine) used ...

Arithmetic logical Irreversibility and the Turing's Halt Problem

The Turing machine halting problem can be explained by several factors, ...

Constructive Many-one Reduction from the Halting Problem to Semi-unification (Extended Version)

Semi-unification is the combination of first-order unification and first...

Recursed is not Recursive: A Jarring Result

Recursed is a 2D puzzle platform video game featuring treasure chests th...

On low for speed oracles

Relativizing computations of Turing machines to an oracle is a central c...

Logical N-AND Gate on a Molecular Turing Machine

In Boolean algebra, it is known that the logical function that correspon...

Logical reduction of metarules

Many forms of inductive logic programming (ILP) use metarules, second-or...