Discussion
Which of the following are incorrect statements ?
(i) A language L is said to be recursively enumerable if there exists a Turing machine that accepts L
(ii) Let K \(\ge\) 1 be an integer. Any K-tape Turing machine cannot be converted to an equivalent one tape Turing machine
(iii) Every computational process which can be considered to be algorithm can be converted to a Turing machine
Answer: B
Only statement (ii) is incorrect, so the answer is (ii) only.
Statement (ii) is false: for any integer K \(\ge\) 1, a K-tape Turing machine can be converted into an equivalent single-tape Turing machine, which stores the K tapes as tracks on one tape and marks each head position. The simulation is slower, roughly quadratic in time, but accepts the same language.
Statement (i) is the definition of a recursively enumerable language: some Turing machine accepts it. Statement (iii) is the Church-Turing thesis, accepted as true. Options that include (i) or (iii) are therefore wrong.
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