Unambiguous Turing machine

In theoretical computer science, a Turing machine is a theoretical machine that is used in thought experiments to examine the abilities and limitations of computers. An unambiguous Turing machine is a special kind of non-deterministic Turing machine, which, in some sense, is similar to a deterministic Turing machine.
Formal definition.
A "non-deterministic Turing machine" is represented formally by a 6-tuple, formula_1, as explained in the page "non-deterministic Turing machine".
An "unambiguous Turing machine" is a non-deterministic Turing machine such that, for all input "w" = "a"1"a"2 ... "an", there exists at most one sequence of configurations "c"0,"c"1, ..., "cm" with the following conditions:
In other words, if "w" is accepted by "M", there is exactly one accepting computation.
Expressivity.
A (deterministic) Turing machine is an unambiguous Turing machine. Indeed, for each input, there is exactly one computation possible.
On the one hand, unambiguous Turing machine have the same expressivity as a Turing machine. Indeed, they are a subset of non-deterministic Turing machines, which have the same expressivity as Turing machines.
On the other hand, unambiguous non-deterministic polynomial time is suspected to be strictly less expressive than non-deterministic polynomial time.
References.
Lane A. Hemaspaandra and Jorg Rothe, "Unambiguous Computation: Boolean Hierarchies and Sparse Turing-Complete Sets", SIAM J. Comput., 26(3), 634–653