Question

Draw a parse tree for the string “big Jim ate green cheese” in ? = (?, ∑, ?, ?, ), where: ? = {?, ?, ?, ?, ?} ∪ ∑ , ∑ = {???, ???, ?????, ?ℎ????, ???}, ? = {? → ?, ? → ??, ? → ???, ? → ???, ? → ?????, ? → ?ℎ????, ? → ???, ? → ???}.

Answer 1

Given that ? = (?, ∑, ?, ?, ), where: ? = {?, ?, ?, ?, ?} ∪ ∑ , ∑ = {???, ???, ?????, ?ℎ????, ???}, ? = {? → ?, ? → ??, ? → ???, ? → ???, ? → ?????, ? → ?ℎ????, ? → ???, ? → ???}

S={S} i.e. S is the start symbol.

Each production is in the form of Aàα   where α € (?, ∑)*

Hence the given grammar is context free grammar.

Now we need construct a parse tree for the string “big Jim ate green cheese”

left most derivation of the given string:

            S-->P V P

-->A P V P                             (using P-->AP)

-->big P V P                           (using A-->big)

-->big N V P                           (using P-->N)

-->big Jim V P                        (using N-->Jim)

-->big Jim ate P                     (using V-->ate)

-->big Jim ate A P                 (using P-->AP)

-->big Jim ate green P          (using A-->green)    

-->big Jim ate green N         (using P-->N)

-->big Jim ate green cheese           (using N-->cheese)

Hence the given string is derived.

parse tree:

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