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Question 1. The following CFG in Chomsky normal form generates strings of balanced parentheses: V1 ? V2V2 | V4V3 | V4V5 | ? V2 ? V2V2 | V4V3 | V4V5 V3 ? V2V5 V4 ? ( V5 ? ) 1. Recall that CYK running on a grammar with r variables and an input string w of length n populates an n x n x r array such that P[l, s, i] is true if and only if variable Ri derives ws ... ws+l-1, the input substring of length l starting at index s. For the grammar above and input w = (())(()()), give a true false answer describing the contents of each of the following cells: P[1, 4, 5] = P[1, 5, 3] = P[5, 2, 1] = P[9, 2, 3] = Hint: Note that you do not need to run the whole algorithm to infer the subproblem answers.

          Question 1. The following CFG in Chomsky normal form generates strings of balanced parentheses:
V1 ? V2V2 | V4V3 | V4V5 | ?
V2 ? V2V2 | V4V3 | V4V5
V3 ? V2V5
V4 ? (
V5 ? )

1. Recall that CYK running on a grammar with r variables and an input string w of length n populates an n x n x r array such that P[l, s, i] is true if and only if variable Ri derives ws ... ws+l-1, the input substring of length l starting at index s. For the grammar above and input w = (())(()()), give a true false answer describing the contents of each of the following cells:
P[1, 4, 5] =
P[1, 5, 3] =
P[5, 2, 1] =
P[9, 2, 3] =

Hint: Note that you do not need to run the whole algorithm to infer the subproblem answers.

Question 1. The following CFG in Chomsky normal form generates strings of balanced parentheses:
V1 ? V2V2 | V4V3 | V4V5 | ?
V2 ? V2V2 | V4V3 | V4V5
V3 ? V2V5
V4 ? (
V5 ? )

1. Recall that CYK running on a grammar with r variables and an input string w of length n populates an n x n x r array such that P[l, s, i] is true if and only if variable Ri derives ws ... ws+l-1, the input substring of length l starting at index s. For the grammar above and input w = (())(()()), give a true false answer describing the contents of each of the following cells:
P[1, 4, 5] =
P[1, 5, 3] =
P[5, 2, 1] =
P[9, 2, 3] =

Hint: Note that you do not need to run the whole algorithm to infer the subproblem answers.

Added by Guillermo C.

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