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CS Theory: Homework
Q1. Show that a one-tape Turing machine that never moves its tape head left is equivalent to a deterministic finite automaton.
Q2. Formally define a Turing machine M that given a binary string on its input tape adds one to it and leaves the result on the input tape. Show the sequence of moves your Turing machine M makes on the input 1011 starting off from the configuration q01011 where q0 is the initial state of M.
Q3. Show that there are potentially nine distinct ways of classifying a language L and its complement L- as being (a) recursive, (b) recursively enumerable but not recursive, and (c) not recursively enumerable. Which of these ways are actually possible?
Q4. Are the recursive languages closed under the Kleene star operator? Briefly justify your answer.
Q5. Is the language L = {wi|Mi does not halt on wi} recursively enumerable? Here wi is an encoding the ith input string and Mi is an encoding of the ith Turing machine. Use reductions and the diagonalization language Ld to prove your answer.
Q6. Is the language L = {M|M does not halt on ∈} recursively enumerable? Here M is an encoding of a Turing machine. Use reductions and the diagonalization language to prove your answer.
Answers in PDF due Nov 12, 2017 on Gradescope. Each problem is worth 20 points. You can discuss problems with others but your answers must be in your own words. Late assignments cannot be accepted.
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