Why Pigeons at Rest Are at the Center of Complexity Theory

Until January 2020, Papadimitriou was thinking about the principle of pigeon for 30 years. So often a joint conversation with a joint head coach was surprised when they caused a simple twist in principle that they never thought of them: if there are fewer pigeons than holes? In this case, any adjustment of pigeons should leave some empty spaces. Still looks open. But have interesting mathematical consequences by inverting the principle of pigeon?

It is as if this “empty-pigeon” principle is only original with an original name. However, this is not a new and productive tool for its delicate different character to categorize the problems of calcification.

To understand the principle of empty pigeon, 3,000 seats from a football stadium, let’s go back to a bank card sample from a smaller two-digit pins. The principle of empty pigeon dictates that some pins are generally represented. If you want to find one of these missing pins don’t look better than asking for each person’s pin. So far, the principle of empty pigeon is like his famous counterpart.

The difference is difficult to check solutions. Imagine that someone says they find two special people at the football stadium in the same pin. In this case, in accordance with the original pigeon scenario, there is a simple way to check this claim: just check it with two people. But in the concert hall, someone claims that no one is 5926 pin. Here it is impossible to check what the pins are asking for the audience. This is more concerned about the theory of complexity of the principle of empty-pigeons.

Two months after Papadimitriou, he started thinking about the principle of empty pigeon and brought a conversation with a potential graduation student. It clearly remembers this because it turned out that Covid-19 talked to everyone with the last person before locking. He collaborated in the house in the coming months and fought the results of problems for the complex theory of the problem. Finally he and his colleagues made a publication paper About the search problems that guarantee solutions due to the principle of empty pigeon. They are particularly interested in the problems where the pigeons are abundant, which are many pigeons. Keep with a tradition Unreasonable acronyms In the theory of complexity, they solved these class problems for “abundant polynomis empty-pigeon principle”.

One of the problems in this class was inspired by the celebrity 70-year-old proof by pionering computer scientist Klost Shannon. Shannon, most of the calculation problems, using an argument that trusts in the principle of empty pigeon must be difficult to solve. However, they did not test computer scientists for decades and could not prove special problems are really difficult. Like the missing bank card pins, there should be difficult problems with the fact that if we cannot identify them.

Historically, researchers not think about the process of searching for difficult problems as a search problem that can be analyzed mathematically. The approach, which grows this process with other search problems related to the principle of papadimitriou, was a flavor characteristics of self-reference Last job In the theory of complexity – a new way of difficulty proving the difficulty of calculating.