 in mathematics and computer science, zeno machines (abbreviated zm, and also called accelerated turing machine, atm) are a hypothetical computational model related to turing machines that allows a countably infinite number of algorithmic steps to be performed in finite time. these machines are ruled out in most models of computation. more formally, a zeno machine is a turing machine that takes 2ân units of time to perform its n-th step; thus, the first step takes 0.5 units of time, the second takes 0.25, the third 0.125 and so on, so that after one unit of time, a countably infinite (i.e. &alefsym;0<!-- \aleph_0 -->) number of steps will have been performed. the idea of zeno machines was first discussed by hermann weyl in 1927; they are named after the ancient greek philosopher zeno of elea (see zeno's paradoxes). zeno machines play a crucial role in some theories. the theory of the omega point devised by physicist frank j. tipler, for instance, can only be valid if zeno machines are possible. == zeno machines and computability == zeno machines allow some functions to be computed that are not turing-computable. for example, the halting problem for turing machines can easily be solved by a zeno machine (using the following pseudocode algorithm): 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 computing of this kind that goes beyond the turing limit is called hypercomputation. it is also an example of a supertask. also, the halting problem for zeno machines is not solvable by a zeno machine (potgieter, 2006). == see also == * hypercomputation * rossâlittlewood paradox * supertask * thomson's lamp * tipler's omega point * zeno's paradoxes == references == *
Hypercomputation Models_of_computation Supertasks Turing_machine