machine has no other way to access this state, for example no node transitions to it. The location of the read-write head is set to zero for at any limit step. Lastly the state of the tape is determined by the limit supremum of previous tape states. For some machine , a cell and, a limit ordinal then That is the th cell at time is the limit supremum of that same cell as the machine approaches . This can be thought of as the limit if it converges or otherwise. Computability Zeno machines have been proposed as a model of computation more powerful than classical Turing machines, based on their ability to solve the halting problem for classical Turing machines. Cristian Calude and Ludwig Staiger present the following pseudocode algorithm as a solution to the halting problem when run on a Zeno machine. begin program write 0 on the first position of the output tape; begin loop simulate 1 successive step of the given Turing machine on the given input; if the Turing machine has halted then write 1 on the first position of the output tape and break out of loop; end loop end program By inspecting the first position of the output tape after unit of time has elapsed we can determine whether the given Turing machine halts. In contrast Oron Shagir argues that the state of a Zeno machine is only defined on the interval , and so it is impossible to inspect the tape at time . Furthermore since classical Turing machines don't have any timing information, the addition of timing information whether accelerating or not does not itself add any computational power. Infinite time Turing machines however, are capable of implementing the given algorithm, halting at time with the correct solution, since they do define their state for transfinite steps. All sets are decidable by Infinite time Turing machines, and sets are semidecidable. Zeno machines cannot solve their own halting problem. See also Computation in the limit Specker sequence Ross–Littlewood paradox References Models of computation Turing machine Hypercomputation Supertasks Articles with example pseudocode