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Unformatted text preview: CS5371 Theory of Computation Homework 3 (Solution) 1. Show that single-tape TMs that cannot write on the portion of the tape containing the input string recognize only regular languages. Answer: Let M = ( Q, Σ , Γ ,q ,q accept ,q reject ) be a single-tape TM that cannot write on the input portion of the tape. A typical case when M works on an input string x is as follows: the tape head will stay in the input portion for some time, and then enter the non-input portion (i.e., the portion of the tape on the right of the | x | th cells) and stay there for some time, then go back to the input portion, and stay there for some time, and then enter the non-input portion, and so on. We call the event that the tape head switches from input portion to non-input portion an out event, and the event that the tape head switches from non-input portion to input-portion an in event. Let first x denote the state that M is in just after its first “out” event (i.e., the state of M when it first enters the non-input portion). In case M never enters the non-input portion, we assign first x =...
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- Spring '10