Hw6 - Homework 6  CISC 303 Timo Kötzing (tkoe@udel.edu)...

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Unformatted text preview: Homework 6  CISC 303 Timo Kötzing (tkoe@udel.edu) Monday, April 5. Friday, April 10. Handed out: Due Date: (8 points) Let A = {a, b}. Give two CFGs accepting L0 and L1 as dened just below, respectively. Problem 1. (i) L0 = {w ∈ A∗ | w = wR } is the set palindromes (words that read the same forwards as backwards). (ii) L1 = {an bk c2n | n, k ≥ 1}. (8 points) Let A = {3, 5, +, ×}, N = {E }. Let P contain all and only the following productions. Problem 2. E → E×E (1) E → E+E (2) E →3 (3) E →5 (4) Let G = (A, N, P, E ). (i) Give ve dierent derivation trees for 3 × 5 + 5 × 3. (ii) For each derivation tree from (i), give the corresponding left-most derivation. (iii) For each derivation tree from (i), give the corresponding right-most derivation. Problem 3. (8 points) Give algorithms dotProductCFG and KleeneStarCFG as follows. (i) dotProductCFG takes two CFGs G0 and G1 and return a CFG G such that L(G ) = L(G0 ) · L(G1 ). (ii) KleeneStarCFG takes a CFG G and return a CFG G such that L(G ) = L(G0 )∗ . Show the result of your algorithm for dotProductCFG on Examples 2.4.2 and 2.4.3 in the Lecture Notes, and show the result of your algorithm for KleeneStarCFG on Example 2.4.2. Note: This last assignment to apply your algorithm is also for you to make sure that your algorithm works; so, please examine the result of your algorithms critically. (8 points) Give an algorithm that takes a CFG G as input and returns a CFG G such that Problem 4. L(G ) = L(G)R . Reminder: For any language L, LR denotes the set of all elements of L reversed: LR = {wR | w ∈ L}. 1 ...
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