Let PrefRep be the set of all languages AE that are prefix-repetitive, by which we mean...

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Let PrefRep be the set of all languages AE that are prefix-repetitive, by which we mean that there are infinitely many strings we Σ* such that ww XA. (a) Prove that μ(Pref Rep|DEC) = 0. (b) Prove that PrefRep is comeager in DEC. Hence the set of decidable, prefix-repetitive languages is a small subset of DEC in the sense of Lebesgue measure, but a large subset of DEC in the sense of Baire category. Let PrefRep be the set of all languages AE that are prefix-repetitive, by which we mean that there are infinitely many strings we Σ* such that ww XA. (a) Prove that μ(Pref Rep|DEC) = 0. (b) Prove that PrefRep is comeager in DEC. Hence the set of decidable, prefix-repetitive languages is a small subset of DEC in the sense of Lebesgue measure, but a large subset of DEC in the sense of Baire category.

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Part a To prove that uPrefRep DEC 0we need to show that the probability of a prefixrepetitive langua... View the full answer