Why computer scientists need magic 8 oracles similar to a ball

The original version to this story appears in How many magazineS

Pose a question in a magical 8 ball and will answer yes, no, or something annoyingly indecisive. We think about it as a toy, but theoretical computer scientists use a similar tool. They often imagine that they can consult with hypothetical devices called oracles that can immediately and correctly answer specific questions. These fantastic thought experiments have inspired new algorithms and helped researchers map the landscape of calculations.

Researchers who refer to oracles work in a computer science, called the theory of computing complexity. They deal with the inherent difficulty of problems such as determining the Dali number is a first -time or finding the shortest path between two points in a network. Some problems are easy to solve, others look much more difficult but have solutions that are easy to check while others are easy for Quantum computers But at first glance, it is difficult for ordinary ones.

Complexity theorists want to find out if these obvious differences in difficulty are basic. Is there anything inherent in certain problems or are we just not smart enough to come up with a good solution? Researchers turn to such questions by sorting the problems in “classes“-All easy problems go in one class, for example, and all easy-to-check problems go to another-and prove theorems about the links between these classes.

Unfortunately, mapping the landscape of computing difficulties turned out to be good, difficult. Thus, in the mid-1970s, some researchers began to study what would happen if the calculation rules were different. That’s where oracles enter.

Like Magic 8 balls, oracles are devices that immediately answer questions yes or no without revealing anything about their internal work. Unlike Magic 8 balls, they always say either yes or not, and they are always right – the advantage of being invented. In addition, any Oracle will only answer a specific type of question, such as “Prime is this number?”

What makes these fictional devices useful for understanding the real world? In short, they can reveal hidden connections between different classes of complexity.

Get the two most famous classes of complexity. There is a class of problems that are easy to solve that researchers call “P”, and the class of problems that are easy to check that researchers call “NP”. All easy -to -check problems are also easy to solve? If so it would mean that NP will equal to P and all encryption will be Cracked (among other consequences). Complexity theoretics suspect that NP does not equal to P but they cannot prove it even though they try to determine the relationship between the two classes for over 50 yearsS

Oracles helped them better understand what they were working with. Researchers have invented oracles that answer questions that help to solve many different problems. In a world where each computer had a hot line to one of these oracles, all easy -to -check problems would also be easy to solve and P would be equal to NP. But other, less useful oracles have the opposite effect. In a world inhabited by these oracles, P and NP would be proven different.