Unformatted text preview: w } . (a) (5%) Give an example of a DFA that is in S . (b) (20%) Show that S is decidable. 4. (20%) Let PAL DFA = {h M i  M is a DFA that accepts some palindrome } . Show that PAL DFA is decidable. (Hint: Prob 2.18 and Prob 4.23 are helpful here.) 5. (20%) Suppose that we have a decider D that decides if the language of a CFG is inﬁnite. That is, D is a decider for the language: INFINITE CFG = {h G i  G is a CFG and L ( G ) is inﬁnite } . By using D or otherwise, show that the following language: C CFG = {h G,k i  G is a CFG and L ( G ) contains exactly k strings where k ≥ 0 or k = ∞} is decidable. 6. (Further studies: No marks) Let C be a language. Prove that C is Turingrecognizable if and only if a decidable language D exists such that C = { x  ∃ y ( h x,y i ∈ D ) } . 1...
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 Spring '10
 H.F.
 Contextfree grammar, 0PDA

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