Provide a context-free grammar for each of the following languages:
The set of strings of base-8 numbers.
The set of strings of base-16 numbers.
The set of strings of base-1 numbers.
Design a language that allows specification of strings of
base-1, base-8, and base-16 numbers, where numbers of a given
type can be syntactically distinguished. Provide a grammar for
this language.
Show a derivation of
( Plus ( Plus a a ) a )
using the grammar:
E -> ( Plus E E )
| ( Minus E E )
| a
Show all distinct derivations (trees) of
a + a + a
using the grammar:
E -> E + E
| a
For the grammar below, describe its associated language:
A -> x A x
| lambda
What are the difficulties associated with constructing a grammar
whose generated strings are decimal representations of irrational
numbers? How can these difficulties be resolved?