Final answer:
To derive the string '0100110' from the given grammar, a sequence of grammar rule applications is used, starting with the symbol S and systematically applying the rules to construct the final string. The derivation process involves several steps and creates a derivation tree that visually represents the formation of '0100110'.
Step-by-step explanation:
Derivation of the string '0100110' using the given grammar
To derive the string '0100110' from the given grammar rules, we need to construct a derivation tree that represents the series of production rules applied to reach the final string. A derivation tree visually represents every step taken to form strings from the starting symbol by applying the grammar rules. The given grammar rules are S ➔ OS | 1AA, A ➔ 0 | 1A | OB, B ➔ 1 | OBB. Here is the derivation sequence for '0100110':
- Start with initial symbol: S
- Apply S ➔ OS resulting in OS
- Apply S ➔ 1AA inside the last S which results in O1AA
- Apply A ➔ 1A to the first A, getting O11AA
- Apply A ➔ OB to the second A, converting it to O11AOB
- Apply A ➔ 0 to the first A, creating O110OB
- Apply B ➔ OBB to B, transforming it into O110OBB
- Apply B ➔ 1 to the first B, leading to O110O1B
- Finally, apply B ➔ 1 to the remaining B, yielding the string '0100110'
By following these steps, we form the given string, and the corresponding derivation tree would branch accordingly to illustrate each application of the rules.