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Which of the following is true for the language {aP | P is a prime}?
- a)It is not accepted by a Turing machine.
- b)It is regular, but not context-free.
- c)It is context-free, but not regular.
- d)It is neither regular nor context-free, but accepted by a Turing machine.
Correct answer is option 'D'. Can you explain this answer?
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Which of the following is true for the language {aP| P is a prime}?a)I...
{aP | P is a prime no. }. This prime number is extra constraint, so this language is neither context free nor regular, but can be accepted by a Turing machine.
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Which of the following is true for the language {aP| P is a prime}?a)I...
Answer:
The language {aP| P is a prime} represents the set of all strings in the form "a" followed by a prime number. We need to determine the nature of this language in terms of regularity and context-freeness.
1. Regular Languages:
Regular languages can be recognized by finite automata, such as deterministic finite automata (DFA) or non-deterministic finite automata (NFA). They can also be represented by regular expressions.
2. Context-Free Languages:
Context-free languages can be recognized by pushdown automata (PDA) or parsed by context-free grammars. They have a more powerful language recognition capability compared to regular languages.
Explanation:
Now, let's analyze the given language {aP| P is a prime} based on the given options:
a) It is not accepted by a Turing machine:
This option implies that the language is not recursively enumerable. However, the language {aP| P is a prime} is recursively enumerable. It is possible to design a Turing machine that enumerates all prime numbers and generates the corresponding strings in the given language.
b) It is regular, but not context-free:
The language {aP| P is a prime} is not regular because prime numbers are not a regular set. Regular languages can only represent regular sets, and the set of prime numbers is not regular.
c) It is context-free, but not regular:
The language {aP| P is a prime} is not context-free. Context-free languages can represent sets that have a nested structure, such as matching parentheses, but prime numbers do not exhibit such a nested structure.
d) It is neither regular nor context-free, but accepted by a Turing machine:
This is the correct option. The language {aP| P is a prime} is neither regular nor context-free. However, as mentioned earlier, it can be recognized by a Turing machine that enumerates prime numbers and generates the corresponding strings "a" followed by those prime numbers.
Therefore, option 'D' is the correct answer.
The language {aP| P is a prime} represents the set of all strings in the form "a" followed by a prime number. We need to determine the nature of this language in terms of regularity and context-freeness.
1. Regular Languages:
Regular languages can be recognized by finite automata, such as deterministic finite automata (DFA) or non-deterministic finite automata (NFA). They can also be represented by regular expressions.
2. Context-Free Languages:
Context-free languages can be recognized by pushdown automata (PDA) or parsed by context-free grammars. They have a more powerful language recognition capability compared to regular languages.
Explanation:
Now, let's analyze the given language {aP| P is a prime} based on the given options:
a) It is not accepted by a Turing machine:
This option implies that the language is not recursively enumerable. However, the language {aP| P is a prime} is recursively enumerable. It is possible to design a Turing machine that enumerates all prime numbers and generates the corresponding strings in the given language.
b) It is regular, but not context-free:
The language {aP| P is a prime} is not regular because prime numbers are not a regular set. Regular languages can only represent regular sets, and the set of prime numbers is not regular.
c) It is context-free, but not regular:
The language {aP| P is a prime} is not context-free. Context-free languages can represent sets that have a nested structure, such as matching parentheses, but prime numbers do not exhibit such a nested structure.
d) It is neither regular nor context-free, but accepted by a Turing machine:
This is the correct option. The language {aP| P is a prime} is neither regular nor context-free. However, as mentioned earlier, it can be recognized by a Turing machine that enumerates prime numbers and generates the corresponding strings "a" followed by those prime numbers.
Therefore, option 'D' is the correct answer.
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Which of the following is true for the language {aP| P is a prime}?a)It is not accepted by a Turing machine.b)It is regular, but not context-free.c)It is context-free, but not regular.d)It is neither regular nor context-free, but accepted by a Turing machine.Correct answer is option 'D'. Can you explain this answer?
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