paradox-driven computers? Has any research been done on paradox-driven computers?

An example of what I mean by "paradox-driven":

Given a computer which can send information back through time, an algorithm to instantly break passwords would be:

crackPassword(){
    String password=recieveFromFuture();
    if (password.checkIfCorrect()){
        sendToPast(password);//no paradox generated, valid password found.
    }else{
        sendToPast(password++);//paradox generated, this "parallel universe" cannot exist.
    }
    return password;
}


Since every parallel universe which does not contain a correct password is impossible, the user will continue on one or more valid "parallel universes".

This allows for the solution of any problem in O(1) time, so long as the answer is easily verified.

To the user this would appear as if the program immediately jumped to a valid password.
This idea, known as Time loop logic has been investigated by Moravec, Deutsch and Aaronson.