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From The Free On-line Dictionary of Computing (05 January 2017) [foldoc]:
Nondeterministic Turing Machine
A normal (deterministic) Turing Machine that
has a "guessing head" - a write-only head that writes a guess
at a solution on the tape first, based on some arbitrary
internal algorithm. The regular Turing Machine then runs
and returns "yes" or "no" to indicate whether the solution is
correct.
A nondeterministic Turing Machine can solve
nondeterministic polynomial time computational {decision
problems} in a number of steps that is a polynomial function
of the size of the input
(1995-04-27)