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Prove that there is no algorithm to decide if a given TM eventually halts if it is started on a blank tape. (HINT: Reduce HALT1 to this problem.) (b) Prove that there is no algorithm to decide if a given TM eventually writes the symbol a if started on a blank tape. (HINT: Reduce the previous problem to this one.) (c) In contrast, prove that there is an algorithm to decide if a given TM eventually writes a non-blank symbol if started on a blank tape.

Prove that there is no algorithm to decide if a given TM eventually halts if it is started on a blank tape. (HINT: Reduce HALT1 to this problem.) (b) Prove that there is no algorithm to decide if a given TM eventually writes the symbol a if started on a blank tape. (HINT: Reduce the previous problem to this one.) (c) In contrast, prove that there is an algorithm to decide if a given TM eventually writes a non-blank symbol if started on a blank tape.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Prove that there is no algorithm to decide if a given TM eventually halts if it is started on a blank tape. (HINT: Reduce HALT1 to this problem.) (b) Prove that there is no algorithm to decide if a given TM eventually writes the symbol a if started on a blank tape. (HINT: Reduce the previous problem to this one.) (c) In contrast, prove that there is an algorithm to decide if a given TM eventually writes a non-blank symbol if started on a blank tape.
Transcribed Image Text:Prove that there is no algorithm to decide if a given TM eventually halts if it is started on a blank tape. (HINT: Reduce HALT1 to this problem.) (b) Prove that there is no algorithm to decide if a given TM eventually writes the symbol a if started on a blank tape. (HINT: Reduce the previous problem to this one.) (c) In contrast, prove that there is an algorithm to decide if a given TM eventually writes a non-blank symbol if started on a blank tape.
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