Question

Find the strings constructed using the derivation trees shown here.

Short answer

A large mathematician hope wildly is the string constructed using the first derivative tree.

“+987” is the string construct using the second derivative tree.

Step-by-step solution

Definition of derivative tree

A derivation in the language generated by a context-free grammar can be represented graphically using an ordered rooted tree, called a derivation, or parse tree.

Firstly, using the phrase-structure grammars.

Suppose \(G = \left( {V, T, S, P} \right)\) is a phrase structure grammar with the starting symbol

\(S = sentence, the set of terminuses.\)

\(T = \left\{ {large, mathematician, hops, a, wildly} \right\}\)

The set of non-terminals

N = {noun phrase, verb phrase, article, adjective, noun, verb, adverb} and productions are

\(\begin{aligned}S \to m, \hfill \\m \to wa \hfill \\l \to h \hfill \\ \end{aligned} \)

(sentence): = (noun phrase)

(Sen tense): = (noun phrase) (verb phrase)

(Noun phrase): = (article noun)

(Transitive verb phrase): = (transitive verb)

(Intransitive verb phrase): = (adverb)

(article): = a

(adjective): = Large

(noun): =mathematician

(Transitive verb): = hops

(adverb): = wildly

Now, we shall find the strings constructed using the derivation trees.

A derivation in the language generated by a context free grammar can be represented graphically using an ordered rooted tree. The root of this tree represents the starting symbol. The internal vertices of the tree represent the non-terminals that arise in the derivation. The leaves of the tree represent the terminal symbols that arise. If the production A à W arises in the derivation, where W is a word, the vertex A has children’s vertices that represent each symbol in W, in order from left to right.

“A large mathematician hope wildly is the string constructed using the above derivative tree.

Hence, “+987” is the string construct using the above derivative tree.