If the strings of a language L can be effectively enumerated in lexico...
L is recursive iff L is enumerable in Lexicographic order (alphabetic).
It is also known that context free language is a subset of recursive languages.
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If the strings of a language L can be effectively enumerated in lexico...
Explanation:
Lexicographic Order:
When the strings of a language L can be effectively enumerated in lexicographic order, it means that the strings are listed in alphabetical order.
Option Analysis:
a) L is necessarily finite:
If the strings of a language L are listed in lexicographic order, it does not necessarily mean that L is finite. It is possible for an infinite language to have its strings listed in lexicographic order.
b) L is regular but not necessarily finite:
If the strings of a language L can be effectively enumerated in lexicographic order, L is regular. Regular languages can have both finite and infinite strings.
c) L is context free but not necessarily regular:
Since lexicographic order implies the strings are listed in a specific order, it does not necessarily mean that the language is context-free. Context-free languages do not have strings listed in a specific order.
d) L is recursive but not necessarily context free:
When the strings of a language L can be effectively enumerated in lexicographic order, the language is recursive. Recursive languages can be infinite and have their strings listed in a specific order. It is not necessary for the language to be context-free.
Therefore, the correct statement is option d) L is recursive but not necessarily context free.