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# CT-G-04 - Graduate Course College of Computer Science...

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Graduate Course THEORY OF COMPUTATION College of Computer Science Final Exam Zhejiang University Fall 2004 Class ID Name Score: Time allowed: 2 Hours. 1. (20%) Determine whether the following statements are true or false. If it is true write a X otherwise a × in the bracket before the statement. (a) ( ) Every context-free language is recursive. (b) ( ) Language { a m b n c l | m, n, l N , m + n > 3 l } is context free. (c) ( ) All languages on an alphabet are recursively enumerable. (d) ( ) There’s a language L such that L is undecidable, yet L and its complement are both semi-decided by the some Turing machine. (e) ( ) There’s a function ϕ such that ϕ can be computed by some Turing ma- chines, yet ϕ is not a primitive recursive function. (f) ( ) Let L 1 , L 2 Σ * be languages, recursive function τ is a reduction from L 1 to L 2 , if L 1 is decidable, then so is L 2 . (g) ( ) A language L is recursive if and only if it is Turing-enumerable. (h) ( ) Every language in NP is recursive.

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