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If the strings of a language L can be effectively enumerated in lexicographic (i.e. alphabetic) order which of the following statements is true?
  • a)
    L is necessarily finite
  • b)
    L is regular but not necessarily finite
  • c)
    L is context free but not necessarily regular
  • d)
    L is recursive but not necessarily context free
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
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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Most Upvoted Answer
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.
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If the strings of a language L can be effectively enumerated in lexicographic (i.e. alphabetic) order which of the following statements is true?a)L is necessarily finiteb)L is regular but not necessarily finitec)L is context free but not necessarily regulard)L is recursive but not necessarily context freeCorrect answer is option 'D'. Can you explain this answer?
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If the strings of a language L can be effectively enumerated in lexicographic (i.e. alphabetic) order which of the following statements is true?a)L is necessarily finiteb)L is regular but not necessarily finitec)L is context free but not necessarily regulard)L is recursive but not necessarily context freeCorrect answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about If the strings of a language L can be effectively enumerated in lexicographic (i.e. alphabetic) order which of the following statements is true?a)L is necessarily finiteb)L is regular but not necessarily finitec)L is context free but not necessarily regulard)L is recursive but not necessarily context freeCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the strings of a language L can be effectively enumerated in lexicographic (i.e. alphabetic) order which of the following statements is true?a)L is necessarily finiteb)L is regular but not necessarily finitec)L is context free but not necessarily regulard)L is recursive but not necessarily context freeCorrect answer is option 'D'. Can you explain this answer?.
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