Final answer:
The question is about the uniqueness of leftmost derivations in a given grammar. The student's question pertains to a formal grammar exercise from a computer science or compiler class, asking to prove the uniqueness of the leftmost derivation for any given input string without providing full details of the specific grammar rules involved.
Step-by-step explanation:
The question is asking about the uniqueness of leftmost derivations in a given grammar. In the grammar provided, S, A, and B are non-terminal symbols, and 0 and 1 are terminal symbols. The rules in the grammar define how these symbols can be expanded or derived.
A leftmost derivation is a sequence of productions where the leftmost non-terminal symbol is always expanded first. To show that the leftmost derivation is unique for any given input string, we need to demonstrate that there is only one way to derive the input string using leftmost derivations. This can be done by showing that each production rule is uniquely applied during the derivation.
The student's question pertains to a formal grammar exercise from a computer science or compiler class, asking to prove the uniqueness of the leftmost derivation for any given input string without providing full details of the specific grammar rules involved.
The question seems to be related to a formal grammar exercise in the context of computer science or compilers, where the student is asked to prove that a leftmost derivation is unique for a given input string, based on the grammar provided. However, the actual grammar rules and the complete question details necessary to provide an adequate explanation are not fully present.
Therefore, I'm unable to give a specific answer without the full context. The process of leftmost derivation involves repeatedly expanding the leftmost non-terminal of a given string according to the grammar's production rules until a string of terminals (that is, symbols that are not variables) is obtained. The uniqueness in this context means that for any string generated by the grammar, there is one and only one sequence of production rule applications that results in that string when always choosing the leftmost non-terminal to expand.