Question

5. Construct the CYK-table for the string aabb using the following grammar: S X Y Z A B + AY | 8 + AY + XZ|XB| b + XB | b → a + b

Answer 1

Answer- Cyk algorithm - FoЯ сак аlgoы +hm qa mая should be in chomiskey Normal Form (CNF). The given grammar given gor SAYIE х-АУ Ys XZ / XB 16 2 X Blb A » a Bb in CNF. is eyk - table- Step-I. n=1w1 - ja abbl -4

Step-2 сак-table - x14- Х3 ТХ- X79 1793 | X34- хи Xo9 33 | Х44- First row variables- Input - aabb х = {A} 722 = {A} 733 Кв, y, z } х4 4 = KB, y, z }

Second row variables ratere- x 12 = X1,822 ={A} {A} ={AA } X 23 - X 92,433 = {A} {By, 2} = AB, AY, AZ) ={six} ¥34 733, 444 - X3,,2} {B,Y,Z} - {BB, BY, BZ, YB, YY, Y2, 2B, 27, 2z}

Third now variables vatere X13=1*11, X23) U (X12, X33) = {A,} {S,x} u{0} {B,X,Z} = 1 AS, AX, BV, *24 = (492, X34) U (423, *44) = { AMO ? uks.x}, {B, Y, Z} -YA, SB, SY, SZ, XB, XY, X2} = 4 y, y} Fourth row variable valeres- X14 = (X11, X24) U (712,X34) U ( *13.844) - {A}, yv,y} U{},{0} _{0}{B,Y,Z} - Kay, ay, B, y, z }

KAZILAY (BY,Z) By,Z} адь ь Therefore storing aabb E L(G).