I can write char a[] = "hello world"; , but i can not write
char a[];
a = "hello world";
why so?

char a[] = "hello world";

you can that because the compiler knows how much space to allocate for the string "hello world."

char a[];
a = "hello world";

C won't allow aggregate assignment; you've got an array of chars and a string, which aren't exactly the same thing. you've also got an unknown size - the compiler doesn't know much space to allocate to a.

char a[80];
strcpy(a, "hello world");

An interesting feature of C though is you can assign structs.

typedef struct {
   char a[40];
} test;

test t1 = { "hello world" }, t2 = t1;

puts(t1.a);
puts(t2.a);

HTH