Symbol Reduction of Turing Machine

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Theorem

Let $T$ be a Turing machine with input symbols $\Sigma$ and blank symbol $B$.

Then there exists a Turing machine $T'$ such that:

  • The input symbols of $T'$ are $\Sigma$
  • The tape symbols of $T'$ are $\Sigma \cup \set B$
  • The language accepted by $T'$ is exactly the language accepted by $T$
  • The inputs on which $T'$ halts are exactly the inputs on which $T$ halts

Proof


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Sources

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