Discuss the decidability/undecidability of the following problem.
Given Turing Machine , state of and string ∈Σ∗, will input ever enter state ?
Formally, is there an such that (,⊢,0)→*(,,)?

Answers

Answer 1

Note that in the caseof the problem described, there is no algorithm that can determine with certainty whether   a given Turing machine, state, and input string will ever enter a specific state.

How is this so?

The problem of determining whether a given Turing machine, state, and string will ever enter a specific state is undecidable.

Alan Turing's   halting problem proves that thereis no algorithm that can always provide a correct answer for all inputs.

Due to the complex and unpredictable   behavior of Turing machines, it is impossible todetermine if a state will be reached in a general case.

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