But how much more difficult? In 1962, the mathematian Tibor Radó invented a new way of exploring this question through what he called The busy beaver game. To play, start by choosing a specific number of rules – Call this number n. Your goal is to find the n-Rule Touring Machine that manages the longest before the event. This machine is called the occupied beaver and the corresponding occupied caster number, BB (n), Is the number of steps it takes.
In principle, if you want to find the beaver busy for any nYou just need to do little. First of all, list as much as possible n-Rule Turing Machines. Then use a computer program to simulate the execution of each machine. Look for the revealing signs that the machines will never stop – for example, many machines will fall into infinite repetitive loops. Discard non-Mint machines. Finally, save the number of steps of all the other Haling front machines. The one with the longest execution time is your animated beaver.
In practice, it becomes difficult. To start, the number of possible machines grows quickly with each new rule. Analyzing them all individually would be hopeless, so you will have to write a personalized computer program to classify and eliminate machines. Some machines are easy to classify: they stop quickly or fall into easily identifiable endless curls. But others run for a long time without displaying an obvious scheme. For these machines, the problem of stopping its formidable reputation.
The more rules you add, the more computer power you need. But the brute force is not surrounded. Some machines work so long before simulating step by step is impossible. You need intelligent mathematical stuff to measure their racing times.
“Technological improvements are definitely helping,” said Shawn LigockiAt the software engineer and the longtime animated beaver hunter. “But they only help I know.”
End of an era
The busy beavers’ hunters began to wrest the BB (6) problem seriously in the 1990s and 2000s, during an impasse in the BB hunt (5). Among them, Shawn Ligocki and his father, Terry, an applied mathematician who directed their research program during resting hours on powerful computers at Lawrence Berkeley National Laboratory. In 2007, they found in a six rules tour machine which broke the record for the greatest execution time: the number of measures it took before Haling had nearly 3,000 figures. It is a colossal number by any ordinary measure. But it is not too big to write. In 12 points, these 3,000 figures will cover about a single sheet of paper.
Three years later, in a undergraduate Slovak student in computer science named Pavel Kropitz decided to tackle the BB (6) hunting as a senior thesis project. He wrote his own research program and configured it to run in the background on a network of 30 computers in a university laboratory. After a month, he found a machine that ran much longer than that discovered by the Ligockis – a new “champion”, in the jargon of busy beavers.
“I was lucky, because the people of the laboratory already complained of my use of the processor and I had to go back a little,” wrote Kropitz in an exchange of direct messages on the Busy Chartor Disitage Server occupied. After another month of research, he broke his own record with a machine whose execution had more than 30,000 figures – Aenough to fill around 10 pages.
