Randomized algorithmA randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are random variables.
Euclidean spaceEuclidean space is the fundamental space of geometry, intended to represent physical space. Originally, that is, in Euclid's Elements, it was the three-dimensional space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces when one wants to specify their dimension. For n equal to one or two, they are commonly called respectively Euclidean lines and Euclidean planes.
Undecidable problemIn computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm that always leads to a correct yes-or-no answer. The halting problem is an example: it can be proven that there is no algorithm that correctly determines whether arbitrary programs eventually halt when run. A decision problem is a question which, for every input in some infinite set of inputs, answers "yes" or "no"..
Striking clockA striking clock is a clock that sounds the hours audibly on a bell, gong, or other audible device. In 12-hour striking, used most commonly in striking clocks today, the clock strikes once at 1:00 am, twice at 2:00 am, continuing in this way up to twelve times at 12:00 mid-day, then starts again, striking once at 1:00pm, twice at 2:00 pm, up to twelve times at 12:00 midnight. The striking feature of clocks was originally more important than their clock faces; the earliest clocks struck the hours, but had no dials to enable the time to be read.
