The diagonal construction used to separate complexity classes requires that a machine can simulate another within bounded space, but this simulation adds a constant-factor overhead.

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Bounded space(alternative to infinite, unbounded space): Space that has limits or edges, like a ball or a closed container, as opposed to space that goes on forever.
Complexity classes(as used in computer science and philosophy of computation): In computer science, groups of problems sorted by how hard they are to solve—roughly, how much computing power and time they require.
Constant-factor overhead(as used in computational analysis): Extra resources (like memory or time) needed for a task that grows at the same rate as the original problem, rather than growing exponentially—for example, needing twice as much memory is a constant-factor overhead.
Machine simulation(as used in computer science): When one computer or abstract computing device runs a program that mimics exactly how another computer would behave, step by step.

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