Show a context-free grammar for each of the following lar Example 1: {a¹bm: m > n, m-n is even} Context-free grammar for the language: S-> aSb S-> Sbb S-> € Example 2: {aibi: i, j≥0 and 2i = 3j + 1} Context-free grammar for the language: S->aaaSbb S -> aab

Formal language

Context-Free Grammar (CFG)

Construct a context-free grammar that generates the language L = {anbmambn |n, m ∈N}.List all variables (non-terminals) and all terminal symbols of your grammar. Also list all production rules.

Context Free Grammar State whether it is ambiguous or unambiguous. If it is ambiguous give an equivalent unambiguous grammar. If it is unambiguous, state all the precedences and associativities enforced by the grammar. <E > -> <F > ∩ <E > | <F > ∪ <E > | <F ><F > -> <F > ∧ <G > | <F > ∨ <G > | <G ><G > -> N | ( <E >)

1. Give a context-free grammar generating the following language (Σ= {a, b, #}): {w#x | the reverse of w is a substring of x for w, x = {a, b}*} 2. Give a context-free grammar that generates the following language! k≥ 2, each x; Є {a, b}*, and for X1 some i and ji, x₁ = x R (= {a, b, #} and x denotes the reverse of xj.) 3. Give a pushdown automaton recognizing the following language: {w the length of w is odd and the middle symbol is a 0} (Σ= {0,1}) 4. Prove the following language is context-free: {x#y | x, y = {a, b}* and x y} (Σ= {a, b, #}) MacBook Air

Convert the following context-free grammar G to an equivalent PDA, where Σ = {a,b} and V = {A,X,Y} with starting variable A (please show the illustrated equivalent PDA): A-> X YX-> a X | aY-> b Y | ε

The following is a context-free grammar G: V={A,B,C} S={a,b} vO=S S->A A alb| A B A->B S ala B->B al\e Convert G into an equivalent context-free grammar in Chomsky normal form. a) Show your grammar rules after Step 1 b) Show your grammar rules after Step 2 c) Show your grammar rules after Step 3 d) Show your grammar rules after Step 4

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Provide the rules for context-free grammars that generate the following languages. L3 = {w ∈ {0, 1}  | n0(w) ≥ 2, and n1(w) is odd}