The halting problem and the universal machine introduced in Sections 11.3 and 11.4 were concerned only with the halting of Turing machines. Consequently, the representation scheme $R(\mathrm{M})$ did not encode accepting states. a) Extend the representation $R(\mathrm{M})$ of a Turing machine $\mathrm{M}$ to explicitly encode the accepting states of $\mathrm{M}$. b) Design a universal machine $\mathrm{U}_f$ that accepts input of the form $R(\mathrm{M}) w$ if the machine $\mathrm{M}$ accepts input $w$ by final state.

   The halting problem and the universal machine introduced in Sections 11.3 and 11.4 were concerned only with the halting of Turing machines. Consequently, the representation scheme $R(\mathrm{M})$ did not encode accepting states.
a) Extend the representation $R(\mathrm{M})$ of a Turing machine $\mathrm{M}$ to explicitly encode the accepting states of $\mathrm{M}$.
b) Design a universal machine $\mathrm{U}_f$ that accepts input of the form $R(\mathrm{M}) w$ if the machine $\mathrm{M}$ accepts input $w$ by final state.

Languages and Machines: An Introduction to the Theory of Computer Science

Thomas A. Sudkamp 2nd Edition

Chapter 11, Problem 10

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- Assume the original representation $ R(\mathrm{M}) $ encodes the states, alphabet, transition function, and the initial state of a Turing machine $ \mathrm{M} $. - To include the accepting states, we modify $ R(\mathrm{M}) $ to also include a list of Show more…

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The halting problem and the universal machine introduced in Sections 11.3 and 11.4 were concerned only with the halting of Turing machines. Consequently, the representation scheme $R(\mathrm{M})$ did not encode accepting states. a) Extend the representation $R(\mathrm{M})$ of a Turing machine $\mathrm{M}$ to explicitly encode the accepting states of $\mathrm{M}$. b) Design a universal machine $\mathrm{U}_f$ that accepts input of the form $R(\mathrm{M}) w$ if the machine $\mathrm{M}$ accepts input $w$ by final state.

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