Linear Grammar and Non-Terminals

Linear grammar is a type of formal grammar used in computer science, linguistics, and communication theory. It is a type of context-free grammar where each production rule has only one non-terminal symbol on the left-hand side and a string of terminals and non-terminals on the right-hand side.

Non-terminal symbols are symbols that stand for classes of phrases or sentence fragments. They are symbols that appear in the grammar rules but do not appear in the final sentences or phrases generated by the grammar. Non-terminals are often represented by capital letters or other symbols.

Multiple Non-Terminals in Linear Grammar

The statement "Linear grammar has more than one non-terminal on the right-hand side" is true. In a linear grammar, each production rule has only one non-terminal on the left-hand side, but the right-hand side can have multiple non-terminals.

For example, consider the following linear grammar:

S → aB
B → bC
C → cD
D → dE
E → e

In this grammar, each production rule has only one non-terminal on the left-hand side, but the right-hand side of each rule has multiple non-terminals. For example, the rule B → bC has two non-terminals on the right-hand side (B and C).

Conclusion

In summary, linear grammar is a type of context-free grammar where each production rule has only one non-terminal symbol on the left-hand side. However, the right-hand side of each rule can have multiple non-terminals. Therefore, the statement "Linear grammar has more than one non-terminal on the right-hand side" is true.

Linear Grammar and Non-Terminals

Linear grammar is a type of formal grammar that allows the generation of linear sequences of symbols. In a linear grammar, each production rule has only one non-terminal on the left-hand side.

The left-hand side of a production rule is the non-terminal symbol that is being replaced, while the right-hand side is the sequence of symbols that replaces the non-terminal. The right-hand side can contain both terminals (symbols that appear in the final output) and non-terminals (symbols that can be replaced by other symbols).

Multiple Non-Terminals in Linear Grammar

Contrary to the statement in the question, it is possible for a linear grammar to have more than one non-terminal on the right-hand side of a production rule. In fact, if a linear grammar only allowed for a single non-terminal on the right-hand side, it would be severely limited in its expressive power.

Consider the following example of a linear grammar with multiple non-terminals:

S → AB
A → aA | ε
B → bB | ε

In this grammar, the start symbol S can be replaced with the sequence AB. The non-terminals A and B can be replaced by their own productions, which may include additional instances of the same non-terminal symbol. For example, the production rule A → aA allows for the insertion of the terminal symbol a before another instance of the non-terminal A.

Conclusion

In summary, linear grammar allows for the generation of linear sequences of symbols, and each production rule has only one non-terminal on the left-hand side. However, it is possible for a linear grammar to have more than one non-terminal on the right-hand side of a production rule, which allows for more complex and expressive grammars.