Is the given grammar ambiguous?

Consider the grammar: as∣asbs∣e. Is this grammar ambiguous? Show that the string 'aab' has two parses.

a) Yes, grammar is ambiguous

b) No, grammar is not ambiguous

c) Ambiguity depends on context

d) Can't determine ambiguity

Final answer:

The grammar as∣asbs∣e is ambiguous because the string 'aab' can have two different parses, indicating multiple parse trees for the same string. Therefore, the correct answer is option A.

Explanation:

The grammar mentioned, as∣asbs∣e, is ambiguous. This is because the string 'aab' can be parsed in two distinct ways using this grammar. Let's illustrate this by showing the two possible parses:

1. Parse one: aab = as (where s = ab)
2. Parse two: aab = asbs (where s = e and b = a)

In the first parse, the grammar generates the string by choosing the first option 'as' and setting s to 'ab'. In the second parse, it chooses the second option 'asbs', sets s to 'e' (the empty string), and b to 'a', generating the string 'aa' by the 'b' being interpreted as 'a' and the 's' being empty.

The fact that we have two different parse trees for the same string is a clear indication that the grammar is ambiguous.