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# asg5 - (a 00(b 000111 1(c 00111 3(6 points The following is...

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Applied Computer Science II Winter semester 2001/2002 Exercise sheet 5 Institut f¨ur Informatik, Albert-Ludwigs-Universit¨ at Freiburg. Date: 21.11.2001 Deadline: 28.11.2001 (before the lecture) 1. (4 points) Examine the formal definition of a Turing machine (Definition 3.1) in the text book. Based on this definition, answer the following questions. Explain your reasons. (a) Can a Turing machine ever write the blank symbol on its tape? (b) Can the tape alphabet Γ be the same as the input alphabet Σ? (c) Can a Turing machine’s head ever be in the same location in two succes- sive steps? (d) Can a Turing machine contain just a single state? 2. (5 points) Consider the following state diagram for a deterministic Turing machine with input alphabet Σ = { 0 , 1 } , tape alphabet Γ = { 0 , 1 , , α, β } . C B D A 1 β, L 0 α, R 0 , β R β R 0 , β L α R β R q accept R q reject , α R 1 , , α R 1 , R 0 , 1 , α R Give the sequence of configurations of this TM for the input strings. In each case, state whether the input string is accepted or rejected.

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Unformatted text preview: (a) 00 (b) 000111 1 (c) 00111 3. (6 points) The following is a state diagram for a non-deterministic Turing machine with input alphabet Σ = { , 1 } , tape alphabet Γ = { , 1 , } , accept state C . C B A → 1 ,R → R 1 → ,R → R 1 → R → L 1 → L Write the conﬁgurations that this TM reaches for the following inputs. For each input, state also whether it is accepted by the TM, rejected by the TM or causes the TM to loop. (Since non-determinism is involved, you should indicate branching with a tree.) (a) 0001 . (b) 010 . (c) 0110 . 4. (5 points) Consider the language L = { w | w contains the same number of s as 1 s } over the alphabet { , 1 } . Design a deterministic Turing machine for that recognizes L . (a) Give implementation-level descriptions of your TM. (b) Draw the state diagram for your TM. — End — 2...
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asg5 - (a 00(b 000111 1(c 00111 3(6 points The following is...

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