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uy mput Si M De d integers. We say that M accepts w in space s if M accepts w after accessing at most the first s cells on its tape, and M accepts w in time t if M accepts w after at most t transitions. (a) Prove that the following langauges are decidable: i. {(M,w) M accepts w in time |w2} ii in onogo lh12)

uy mput Si M De d integers. We say that M accepts w in space s if M accepts w after accessing at most the first s cells on its tape, and M accepts w in time t if M accepts w after at most t transitions. (a) Prove that the following langauges are decidable: i. {(M,w) M accepts w in time |w2} ii in onogo lh12)

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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2. Let M be a Turing machine, let w be an arbitrary input string, and let s and t be positive integers. We say that M accepts w in space s if M accepts w after accessing at most the first s cells on its tape, and M accepts w in time t if M accepts w after at most t transitions. (a) Prove that the following langauges are decidable: i. {(M, w) | M accepts w in time |w|2} ii. {(M,w) M accepts w in space |w|2} (b) Prove that the following languages are undecidable: i. {(M) | M accepts at least one string w in time |w|2} ii. {(M) M accepts at least one string w in space |w|2}
Transcribed Image Text:2. Let M be a Turing machine, let w be an arbitrary input string, and let s and t be positive integers. We say that M accepts w in space s if M accepts w after accessing at most the first s cells on its tape, and M accepts w in time t if M accepts w after at most t transitions. (a) Prove that the following langauges are decidable: i. {(M, w) | M accepts w in time |w|2} ii. {(M,w) M accepts w in space |w|2} (b) Prove that the following languages are undecidable: i. {(M) | M accepts at least one string w in time |w|2} ii. {(M) M accepts at least one string w in space |w|2}
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