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Say that a write-once Turing machine is a single-tape TM that can alter each tape square at most once (including the input portion of the tape). Show that this variant Turing machine model is equivalent to the ordinary Turing machine model.

Short Answer

Expert verified

Variant Turing Machine is similar to the ordinary Turing Machine.

Step by step solution

01

Explain Turing machine

An unconstrained grammar-based computational model called a Turing machine includes Pushdown automata (PDA) and Finite Automata (FA).

02

Step 2: Implement write-once TM using the write-twice TM

First begin by simulating a write-once-and-read-again Turing machine. By transferring the entire tape to a new section of tape to the right of the currently used section, the write-twice machine replicates one step of the original machine. Character by character, the copying process goes about its business, marking each character as it is copied.

Each tape square is altered twice throughout this process: First, write the character and again then indicate that it has been copied. On the tape, there is a mark where the tape head was located on the original Turing computer. The tape content is updated in accordance with the original Turing machine's rules when copying the cells at or near the marked position. Operate as usual when using a write-once machine to run the simulation, with the exception that each cell from the previous tape is now represented by two cells. The first of these contains the tape symbol for the original machine, while the second is for the mark applied during copying. When the tape is copied for the first time, the copying marks are placed over the input symbols because the machine isn't given input in the format with two cells per symbol.

Hence, a write-once TM is created using the write-twice TM to approximate an ordinary TM.

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