part-ii/2021-25/

[tripos-comments[bot]]

Part II 2021 Automata and Formal Languages: Paper 3, Section I, F

https://questions.tripos.org/part-ii/2021-25/

[artie2000]

All bookwork except for the countable case.

Countable case:

No in both cases.

Any finite language is regular, so take (for example) $L_i={p_i}$, the $p^\text{th}$ prime, for a counterexample.

Since the complement of a regular language is regular, we can turn the last counterexample into a counterexample for the countable intersection.