The list: complexityzoo.uwaterloo.ca/Complexity_Zoo

Computational problem where the solution is either yes or no.

When there are more than two possible answers, it is called a function problem.

Decision problems come up often in computer science because many important problems are often stated in terms of "decide if a given string belongs to given formal language".

The canonical undecidable problem.

A Turing machine decider is a program that decides if one or more Turing machines halts of not.

Of course, because what we know about the halting problem, there cannot exist a single decider that decides all Turing machines.

E.g. The Busy Beaver Challenge has a set of deciders clearly published, which decide a large part of BB(5). Their proposed deciders are listed at: discuss.bbchallenge.org/c/deciders/5 and actually applied ones at: bbchallenge.org.

But there are deciders that can decide large classes of turing machines.

Many (all/most?) deciders are based on simulation of machines with arbitrary cutoff hyperparameters, e.g. the cutoff space/time of a Turing machine cycler decider.

The simplest and most obvious example is the Turing machine cycler decider

Bibliography: discuss.bbchallenge.org/t/decider-cyclers/33

Example: bbchallenge.org/279081.

These are very simple, they just check for exact state repetitions, which obviously imply that they will run forever.

Unfortunately, cyclers may need to run through an initial setup phase before reaching the initial cycle point, which is not very elegant.

Also, we have no way of knowing the initial setup length of the actual cycle length, so we just need an arbitrary cutoff value.

And unfortunately, this can lead to misses, e.g. Skelet machine #1, a 5 state machine, has a (translated) cycle that starts at around 50-200M steps, and takes 8 trillion steps to repeat.

Bibliography: discuss.bbchallenge.org/t/decider-translated-cyclers/34

Like a cycler, but the cycle starts at an offset.

To see infinity, we check that if the machine only goes left N squares until reaching the repetition, then repetition must only be N squares long.

Described at: www.sligocki.com/2022/06/10/ctl.html

A nuclear fuel bank is a facility or system created to provide a secure and dependable source of nuclear fuel to countries that may wish to develop nuclear energy but lack the necessary infrastructure to produce their own nuclear fuel. The concept is part of broader non-proliferation efforts aimed at ensuring that nations have access to nuclear fuel for peaceful purposes—such as electricity generation—while preventing the spread of nuclear weapons capabilities.

The busy beaver game consists in finding, for a given $n$, the turing machine with $n$ states that writes the largest possible number of 1's on a tape initially filled with 0's. In other words, computing the busy beaver function for a given $n$.

There are only finitely many Turing machines with $n$ states, so we are certain that there exists such a maximum. Computing the Busy beaver function for a given $n$ then comes down to solving the halting problem for every single machine with $n$ states.

Some variant definitions define it as the number of time steps taken by the machine instead. Wikipedia talks about their relationship, but no patience right now.

The Busy Beaver problem is cool because it puts the halting problem in a more precise numerical light, e.g.:

Bibliography:

B Reactor is a historical nuclear reactor located at the Hanford Site in Washington State, USA. It was the world's first full-scale plutonium production reactor, used during World War II as part of the Manhattan Project. Commissioned in 1944, B Reactor played a crucial role in producing plutonium for atomic bombs, including the bomb dropped on Nagasaki, Japan. B Reactor was designed as a production reactor, using graphite as a moderator and water as a coolant.

The list of nuclear and radiation fatalities by country typically refers to incidents and accidents where radiation exposure has led to fatalities, as well as deaths related to nuclear weapons use. Here are some key events and their associated fatalities: 1. **Hiroshima and Nagasaki, Japan (1945)**: The atomic bombings resulted in immediate deaths of approximately 140,000 in Hiroshima and 74,000 in Nagasaki by the end of that year.

Operation Giant Lance was a Cold War-era military operation conducted by the United States in 1983. Its primary objective was to demonstrate the ability to mobilize U.S. nuclear forces in response to perceived threats from the Soviet Union, particularly in the context of escalating tensions during that time. The operation involved the readiness and potential deployment of nuclear-capable aircraft, submarines, and intercontinental ballistic missiles (ICBMs).

Nuclear bunkers in the People's Republic of China refer to fortified structures designed to protect individuals and critical assets from the effects of nuclear explosions, including radiation, shockwaves, and fallout. These facilities can range from deep underground shelters to reinforced buildings capable of withstanding a nuclear attack.

The nuclear weapons debate refers to the ongoing discussion and contention surrounding the possession, proliferation, and potential use of nuclear weapons. This debate encompasses a variety of perspectives and issues, including: 1. **Proliferation vs. Disarmament**: Advocates argue for nuclear disarmament, seeking to eliminate nuclear weapons and reduce their risks, while others believe that nuclear weapons are essential for national security and deterrence.

"Two Bombs, One Satellite" is a term used to refer to the geopolitical and military dynamics involving China and Taiwan, particularly the implications of China's missile capabilities and space advancements. This phrase became more prominent in discussions about China's military strategy and its impact on U.S. foreign policy, especially in relation to Taiwan. The concept contrasts China's developments in both its ballistic missile technology (the "two bombs")—which includes nuclear and conventional missiles—and its advancements in space capabilities (the "one satellite").

Bertrand Goldschmidt (1920–2018) was a French chemist known for his significant contributions to the fields of chemistry and nuclear physics. He played a key role in the development of nuclear energy and the advancement of various chemical processes. Goldschmidt's work included research on the properties of nuclear materials, nuclear fission, and the implications of nuclear technology for energy production. He is also known for his involvement in public discussions about the safety and ethical aspects of nuclear energy.

Cadarache is a significant nuclear research center located in the south of France, specifically in the Provence region near the town of Saint-Paul-lez-Durance. The site is primarily associated with the French Alternative Energies and Atomic Energy Commission (CEA). Cadarache is known for its focus on nuclear energy research, development, and innovation, particularly in the fields of nuclear reactors, fuel cycle technologies, and advanced materials.

Fort de Châtillon is a historical fortification located in the region of Île-de-France, near the town of Châtillon in France. Built in the late 19th century, it was part of the Séré de Rivières system of fortifications designed to protect Paris from potential attacks, particularly in light of the Franco-Prussian War. The fort played a strategic role in the defense of the capital.

India's three-stage nuclear power programme is a strategic plan developed to utilize its vast nuclear resources for energy production, while also promoting long-term self-sufficiency in nuclear technology. The programme primarily focuses on harnessing the country's thorium reserves, which are among the largest in the world, and it is structured around three key stages: ### Stage 1: Pressurized Heavy Water Reactor (PHWR) - **Fuel**: Natural uranium.