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# tutorial3 - 3515ICT Theory of Computation Tutorial problems...

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3515ICT Theory of Computation Tutorial problems: Turing machines, decidability and undecidability 1. Give implementation level and formal descriptions of a Turing machine to recognise the language L = { a n b n c n | n 0 } . You may assume either a single- or doubly-infinite tape. 2. Give implementation level and formal descriptions of a Turing machine to compute the sum of integers m and n . The input should have the form 1 m +1 01 n +1 , with the head on the leftmost 1, and the output should have the form 1 m + n +1 , with the head again on the leftmost 1. 3. Give an implementation level description of a Turing machine to compute Ackermann’s function, defined by A (0 , n ) = n + 1 , A ( m + 1 , 0) = A ( m, 1) , A ( m + 1 , n + 1) = A ( m, A ( m + 1 , n )) . The input and output should have the same form as in the previous question. (Difficult) 4. (Hopcroft et al. , Exercise 8.4.3) Give implementation level descriptions of nondetermin- istic Turing machines — possibly a multitape machines — that recognise the following languages. Try to exploit nondeterminism to avoid iteration and keep computations short

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tutorial3 - 3515ICT Theory of Computation Tutorial problems...

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