Hypercomputation.info

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.

According to EETimes Europe , Princeton researchers claim quantum computing breakthrough . In particular, they "have developed a technique to read spintronic information off electrons, a potential step on the road to quantum computing." The importance of this development is that it opens the road to quantum computers  with millions of qubits.

Today I discovered yet another proof of the Church-Turing thesis (CTT)! In particular, Ramón Casares in his Proof of Church's Thesis proves the CTT using another more "general" thesis: Persons’ syntax engine is a Finite Universal Turing Machine.  A finite Turing machine is one that has a tape of finite length. Any person has a syntactical capability, that is the ability to speak a language and a syntax engine is a machine with a syntactical capability. So the question is whether there are machines that can really understand languages? Obviously, it is one think to dully manipulate symbols and another to understand the meaning associated to symbols. After all, this was nicely demonstrated with the Chinese Room Argument (in essence, this argument is a "proof" that intelligence cannot be equated with symbol manipulation, and, obviously, it is not an argument "against the possibility of true artificial intelligence"). Now the problem with this proo...

The First International Conference on Logic and Relativity: honoring István Németi's 70th birthday took place in Budapest, last September. The theme of the conference was the connection between logic and relativity theory. Obviously, since Németi initiated what is now called relativistic computing , a number of speakers presented work that falls in this research area. Unfortunately, for a number of good reasons, it was not possible to attend the event, so I cannot give a report of it. Nevertheless, when skimming through the web pages, one can easily see that the event was very interesting. I just hope more events like this will take place.

I had the impression that the Church-Turing thesis has not been proven, but a recent posting to the Arxiv server claimed otherwise. In partricular, Nachum Dershowitz and Evgenia Falkovic in their extended abstract entitled " A Formalization and Proof of the Extended Church-Turing Thesis " claim that they offer a proof of the Extended Church-Turing Thesis: Every effective algorithm can be efficiently simulated by a Turing machine. Interestingly, this proof uses the notion of classical algorithm which is a time-sequential state-transition system, whose transitions are partial functions on its states. But obviously, this is not an algorithm but something that someone calls a classical algorithm. Now if one has a deep desire to prove the Church-Turing thesis, then she can formulate and prove it inside Eff , that is, the effective topos (see Categorical Logic and Type Theory , p. 402)! In a nutshell, no I don't think this paper is a proof of the CTT.

Today I received an e-mail notification about a new book entitled A Computable Universe: Understanding and Exploring Nature as Computation . According to the publisher, the book It focuses on two main questions: What is computation? How does nature compute? Obviously there is an oxymoron here—if one does not know what  computation is, then it makes absolutely no sense to say anything about nature's computational capabilities! Notwithstanding, I find extremely naive the idea of a computable universe. To me it is more science fiction than science. But I have argued against this absurd idea elsewhere, so I will say no more here. PS The book's site states that "contributors are world-renowned experts", in what respect is the editor a world-renowned expert?

Recently, Jérémie Cabessa and Hava T. Siegelmann published a paper entitled The Computational Power of Interactive Recurrent Neural Networks . In this paper, the authors discuss a new form of interactive recurrent neural networks that are able to interact with other systems and/or the environment. These neural networks are shown to be strictly more powerful than interactive Turing machines, which implies that they have hypercomputational capabilities.