Question

Prove that the following BNF grammar is ambiguous.

->
|
|
-> +1-
-> + - *
-> 0|1|2|3|4|5|6|7|8|9
You can draw the parse trees on a piece of paper, and then take a clear picture of your trees using your cell phone and upload the picture. Alternatively, you can just do leftmost derivations to generate the sentence instead of drawing parse trees.

Answer 1

To prove the BNF grammar is ambiguous, it's necessary to show multiple parse trees for the same expression, which result in different interpretations. Without specific BNF rules and examples, the proof by parse trees or derivations can't be provided. Resolving ambiguity in grammars involves defining operator precedence and associativity.

Step-by-step explanation:

To prove that the given BNF grammar is ambiguous, we need to demonstrate that there is more than one way to derive the same string from the grammar, resulting in different parse trees. However, since BNF (Backus-Naur Form) grammars are a method of describing the syntax of a language, which is typically a concept dealt within Computer Science and related fields, we will approach this with respect to parsing expressions in a hypothetical programming language context.

Consider the expression '1 + 2 * 3'. In an ambiguous grammar, this expression can be interpreted in more than one way, leading to different results. A leftmost derivation could parse this expression as '(1 + 2) * 3' or '1 + (2 * 3)'. Both interpretations are valid, but they yield different parse trees and hence different results, which is not desirable in programming languages since the ambiguity can lead to unexpected behavior.

Without the specific BNF rules and a concrete example, we cannot graphically prove the ambiguity through parse trees or derivations. In practice, to resolve ambiguity, the grammar rules need to be refined to enforce a specific order of operations—usually accomplished by defining operator precedence and associativity within the grammar itself