prolog - Right linear context free grammar with even difference of 0's and 1's -

i'm trying write right linear context free grammar, in difference between numbers of 0's , 1's should even. example:

010001 = 4 - 2 = 2 (even)

i had similar problem. maybe help! i'm trying write on prolog. did other 10 exercises difficult me. ideas on how it?

my code

s --> []. s --> [1],a. s --> [0],b.  --> [1],s. --> [0],c.  b --> [1],c. b --> [0],s.  c --> []. c --> [1],b. c --> [0],a.

it's work many cases i'm not sure if well.

the problem can simplified little math.

let a number of 0, b - number of 1, n - length of word. want abs(a - b) even.

do math:

a + b = n b = n - a - b = - n + = 2*a - n

2*a even, abs(a - b) iff n even.

so task check if length of word even.

solution:

s --> []. s --> digit, digit, s. digit --> [0]. digit --> [1].

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