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Consider this Turing Machine M1: 1/1,R /R qr /R 90 94 1/1,R 0/L,R 0/1, R 1/1, R 0/1, R 0/0,R 91 92 1/1,R /,R -/-R ~/~₁L qa 93 0/0,L 1/1,L M computes a partial function F(M) : Σ* → I*. * F(M)(w) = xy if (ɛ, qo, w) →* (x, q, y) where q = {qa, qr} and xy has no at either end. * Otherwise, F(M) is undefined at w. *xy is the contents of the tape when M halts. * ƒ : Σ* → I'* is partially computable if f = F(M) for some TM M. * f : Σ* → I* is computable if f = F(M) for some total TM M. Question: Consider the partial function F(M₁) computed by M₁. What is F(M₁)(0000)? That is, what does M₁ compute for input 0000?

Consider this Turing Machine M1: 1/1,R /R qr /R 90 94 1/1,R 0/L,R 0/1, R 1/1, R 0/1, R 0/0,R 91 92 1/1,R /,R -/-R ~/~₁L qa 93 0/0,L 1/1,L M computes a partial function F(M) : Σ* → I*. * F(M)(w) = xy if (ɛ, qo, w) →* (x, q, y) where q = {qa, qr} and xy has no at either end. * Otherwise, F(M) is undefined at w. *xy is the contents of the tape when M halts. * ƒ : Σ* → I'* is partially computable if f = F(M) for some TM M. * f : Σ* → I* is computable if f = F(M) for some total TM M. Question: Consider the partial function F(M₁) computed by M₁. What is F(M₁)(0000)? That is, what does M₁ compute for input 0000?

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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Consider this Turing Machine M1: 1/1,R /R qr /R 90 94 1/1,R 0/L,R 0/1,R 1/1,R 0/1,R 0/0,R 91 92 1/1,R /,R /R /L qa 93 0/0,L 1/1,L M computes a partial function F(M) : Σ* → I*. * F(M)(w) = xy if (ɛ, qo, w) →* (x, q, y) where q = {qa, qr} and xy has no at either end. * Otherwise, F(M) is undefined at w. *xy is the contents of the tape when M halts. *f: E* → I* is partially computable if f = F(M) for some TM M. * f : Σ* → I* is computable if f = F(M) for some total TM M. Question: U Consider the partial function F(M₁) computed by M₁. What is F(M₁) (0000)? That is, what does M₁ compute for input 0000?
Transcribed Image Text:Consider this Turing Machine M1: 1/1,R /R qr /R 90 94 1/1,R 0/L,R 0/1,R 1/1,R 0/1,R 0/0,R 91 92 1/1,R /,R /R /L qa 93 0/0,L 1/1,L M computes a partial function F(M) : Σ* → I*. * F(M)(w) = xy if (ɛ, qo, w) →* (x, q, y) where q = {qa, qr} and xy has no at either end. * Otherwise, F(M) is undefined at w. *xy is the contents of the tape when M halts. *f: E* → I* is partially computable if f = F(M) for some TM M. * f : Σ* → I* is computable if f = F(M) for some total TM M. Question: U Consider the partial function F(M₁) computed by M₁. What is F(M₁) (0000)? That is, what does M₁ compute for input 0000?
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