Hypercomputation.info

Judit  Madarász and Gergely Székely, in a paper that was recently posted to the arXiv and which is entitled The Existence of Superluminal Particles is Consistent with Relativistic Dynamics , examine whether particles that are supposed to travel faster than the light violate any physical law. Their conclusion is that the existence of particles that travel faster than the light cannot be ruled out by special relativity.  

Selim Akl has convincingly argued that there is no universal computer . This may come to a surprise to people since one of the first things we learn when studying computability theory is the notion of the universal Turing machine. But then again, we learn that there is a thesis that dictates what and what cannot be computed!

In a recent paper  entitled " Bounds on Spectral Dispersion from Fermi-Detected Gamma Ray Bursts ",  Robert J. Nemiroff and his colleagues use scientific data to disprove the idea that space-time is "foamy" at the Planck scale. Apparently, this is really bad news for the aficionados of digital physics, phoilosophy, etc. 

The Active Element Machine is a new model of computation invented by  Michael Stephen Fiske . The model can use a random bit source from the environment to generate an arbitrary real number in the unit interval.  In addition, by using the same randomness, the machine can decide any language L ⊆ {0,1} * . In other words, this machine has capabilities that transcend the capabilities of the Turing machine.

It seems that some people do not understand the connection between hypercomputation and what Mark Burgin calls super-recursive algorithms. According to Burgin, "super-recursive algorithms are algorithms that control hypercomputation." In different words, a method that describes a task that produces a result not computable by a Turing machine is a super-recursive algorithm (or a hyperalgorithm, as I like to call them).

Roughly speaking, Turing has proved that it is not possible to tell whether a computer program will terminate or not. Recently, William Gasarch posted an article to the arXiv in which he shows how one can prove program termination. Gasarch does not disprove Turing, but " discuss various ways to prove that [a] program terminates".

Gentian Kasa has posted to the arXiv a good summary of hypercomputation. His summary is actually his MSc thesis and it is entitled " Hypercomputation: Towards an extension of the classical notion of Computability? " It is quite encouraging to see students work on hypercomputation despite the unfair criticism.