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, , 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 = a1a2... an, there exists at most one sequence of configurations c0,c1,..., cm with the following conditions:
  1. c0 is the initial configuration with input w
  2. ci+1 is a successor of ci and
  3. cm is an accepting configuration.
In other words, if w is accepted by M, there is exactly one accepting computation.

Expressivity

A 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.