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
- 1956: Claude E. Shannon: A Universal Turing Machine with Two Internal States (Automata Studies Ser. Annals of Mathematics Studies Vol. 34: pp. 157 – 165) (edited by C. E. Shannon and J. McCarthy)
Zentralblatt MATH: 0074.11204