Does a (cryptographic?) function to satisfy these 3 constraints exist?

[mihairaulea]

1. f(program, state) = hash. hash is unique for every program, state. f is public.

2. f^-1(hash) does not exist, and there is no way to function g(hash) = (program, state).
Meaning, there is no other way to obtain the hash but by using f.

3. verify(program, state, hash) = true, if f(program, state) = hash. False otherwise.