#Strings DFA

Question

$ L\ =\ \{\ a^mb^{2n}c^{3n}d^p\ |\ m,n\ >=1\ ,\ p\ >\ m\} \\Find\ the\ number\ of\ strings\ of\ length\ <=\ 13$

Comments

i also getting 13.
a bbbb cccccc dd = 1 with 13 length
a bb ccc {dd, ddd,dddd,ddddd,dddddd,,dddddd} = 6 strings till length 13
aa bbccc {ddd,dddd,ddddd,dddddd} = 4 till length 13
aaa bbccc { dddd,ddddd} = 2 till length 13
total = 1+6+4+2= 13

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minimum is 8 length string, we will start from 8 length string.

|w|=8: {(m=1,n=1,p=2)} -> 1 string

|w|=9: {(m=1,n=1,p=3)} -> 1 string

|w|=10 {(m=1,n=1,p=4), (m=2,n=1,p=3)} -> 2 strings

|w|=11: {(m=1,n=1,p=5), (m=2,n=1,p=4)} -> 2 strings

|w|=12: {(m=1,n=1,p=6), (m=2,n=1,p=5), (m=3,n=1,p=4)} ->3 strings

|w|=13 {(m=1,n=1,p=7), (m=2,n=1,p=6), (m=3,n=1,p=5), (m=1,n=2,p=2)} ->4 strings

total-> 1+1+2+2+3+4= 13 strings

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Thanks. 13 is correct.

Answer 1

13 corerect answer

Answer 2

13 correct answer