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In abstract topology, a machine is method for producing infinite loop spaces and spectra. In automata theory, an abstract machine that is implemented in hardware is simply ...

An abstract machine that is implemented in software is termed a virtual machine.

A computation is an operation that begins with some initial conditions and gives an output which follows from a definite set of rules. The most common example are ...

A nondeterministic Turing machine is a "parallel" Turing machine that can take many computational paths simultaneously, with the restriction that the parallel Turing machines ...

Instead of picking two points from the interior of the cube, instead pick two points on different faces of the unit cube. In this case, the average distance between the ...

Graham's biggest little hexagon is the largest possible (not necessarily regular) convex hexagon with polygon diameter 1 (i.e., for which no two of the vertices are more than ...

What is the area of the largest square that can be inscribed on a unit cube (Trott 2004, p. 104)? The answer is 9/8, given by a square with vertices (1/4, 0, 0), (0, 1, 1/4), ...

Given four points chosen at random inside a unit cube, the average volume of the tetrahedron determined by these points is given by ...

A packing of polyhedron in three-dimensional space. A polyhedron which can pack with no holes or gaps is said to be a space-filling polyhedron. Betke and Henk (2000) present ...

There exist lattices in n dimensions having hypersphere packing densities satisfying eta>=(zeta(n))/(2^(n-1)), where zeta(n) is the Riemann zeta function. However, the proof ...