Which of the following option is true?a)Complement of CSL is CSL.b)Com...
Explanation:
The correct answer is option 'A': The complement of the Context-Sensitive Language (CSL) is also a Context-Sensitive Language (CSL).
To understand this, let's first define the concepts involved:
1. Context-Sensitive Language (CSL):
A Context-Sensitive Language is a language that can be generated by a context-sensitive grammar. In a context-sensitive grammar, the production rules are of the form α → β, where α and β are strings of terminals and non-terminals, and the length of α is less than or equal to the length of β. These grammars are more powerful than regular grammars (Regular Languages), context-free grammars (Context-Free Languages), and regular expressions (Regular Languages).
2. Complement of a Language:
The complement of a language L, denoted by L', is the set of all strings that are not in L. In other words, if a string is in L, it is not in L', and vice versa.
Now, let's analyze the options one by one:
a) Complement of CSL is CSL:
This statement is true. The complement of a Context-Sensitive Language (CSL) is also a Context-Sensitive Language (CSL). This is because the class of Context-Sensitive Languages is closed under complementation.
b) Complement of CFL is CFL:
This statement is false. The complement of a Context-Free Language (CFL) is not necessarily a Context-Free Language (CFL). The class of Context-Free Languages is not closed under complementation.
c) Complement of RE is RE:
This statement is false. The complement of a Regular Language (RE) is not necessarily a Regular Language (RE). The class of Regular Languages is not closed under complementation.
d) Complement of non-CFL can't be CFL:
This statement is true. The complement of a non-Context-Free Language (non-CFL) cannot be a Context-Free Language (CFL). The class of Context-Free Languages is not closed under complementation.
Conclusion:
The correct answer to the question is option 'A'. The complement of a Context-Sensitive Language (CSL) is also a Context-Sensitive Language (CSL), and this is because the class of Context-Sensitive Languages is closed under complementation.
Which of the following option is true?a)Complement of CSL is CSL.b)Com...
Context-sensitive Language: The language that can be defined by context-sensitive grammar is called CSL. Properties of CSL are: Union, intersection and concatenation of two context-sensitive languages is context-sensitive. The complement of a context-sensitive language is context-sensitive. CSL closed under complement so the complement of CSL is CSL.
RE and CFL are not closed under complement.
Complement of non-CFL can be CFL i.e. {ww = CSL} complement = CFL.
Hence, the correct option is (A).
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