The “Beaver” challenge, a mathematical puzzle over 30 years old, solved by a team that is part of “the beavers”

2024-07-17 04:00:08

In recent times, listing computer science exploits has been reduced to citing new advances in artificial intelligence. July 2, The announcement of a controversial show over 30 years old came to bear this litany. In addition, the effect, told by the American media Quanta Journal, does not come from either world scholars or industry. It was achieved by an international team of about twenty people, in remote collaboration, in part “apes”, and the Frenchman Tristan Stérin brought together.

Co-Founder of Enterprise Software PRGM, he launched, in March 2022, the challenge of solving a problem that has tired more than one: know which computer system, within a family of more than 16,000 billion, stands to give its answer, effectively eliminating the a “nonsense” program that continues to advertise. The eternal vitamin. And above all, find the rare gem, the one that stands behind the greatest number of steps. The problem was named the “busy beaver race” by the Hungarian mathematician Tibor Rado in 1962, in honor of the animal’s virtues.

“You’re like a Pokémon hunter!” » comedy Tristan Stérin. What is the benefit? This “game”, which describes how complexity emerges from simplicity, involves deep questions in mathematics and computer science.

Turing’s slim

To understand the matter, reminders are necessary. In 1936, the British Alan Turing showed that any program, from the simple “hello” display to the most complex, such as the great ChatGPT and others, can be represented “only” by the machine that bears his name: the ribbon affect. infinite, marked with 0 or 1 when passed under the read/write header. The head can only rotate the symbols 0 or 1, move the ribbon forward or backward one square and change the state. This “state”, which consists of these three instructions (write 0 or 1, move forward/backward, change state), is the software of the device. It can have one, two or more… A single-state machine can do 25 different programs. From one to two, 6,561, and from one to five, more than 16,000 billion.

With this idea, Turing showed that it is impossible to find a program that says whether another program will stop or not. The Problem of the Busy Beaver (” busy beaver » in English or BB for short) shows another weakness: it calculates the largest “useful” setting, which makes the ribbon move the most before stopping and giving the answer. Tibor Rado showed that this function is not computable: it is not possible to find all these values ​​through a series of functions.

You have 57.18% of this article left to read. The rest is reserved for subscribers.