A Hypercomputation in Brouwer's Constructivism

In contrast to other constructivist schools, for Brouwer, the notion of "constructive object" is not restricted to be presented as `words' in some finite alphabet of symbols, and choice sequences which are non-predetermined and unfinished objects are legitimate constructive objects. In this way, Brouwer's constructivism goes beyond Turing computability. Further, in 1999, the term hypercomputation was introduced by J. Copeland. Hypercomputation refers to models of computation which go beyond Church-Turing thesis. In this paper, we propose a hypercomputation called persistently evolutionary Turing machines based on Brouwer's notion of being constructive.Comment: This paper has been withdrawn by the author due to crucial errors in theorems 4.6 and 5.2 and definition 4.

Hard to Cheat: A Turing Test based on Answering Questions about Images

Progress in language and image understanding by machines has sparkled the interest of the research community in more open-ended, holistic tasks, and refueled an old AI dream of building intelligent machines. We discuss a few prominent challenges that characterize such holistic tasks and argue for "question answering about images" as a particular appealing instance of such a holistic task. In particular, we point out that it is a version of a Turing Test that is likely to be more robust to over-interpretations and contrast it with tasks like grounding and generation of descriptions. Finally, we discuss tools to measure progress in this field.Comment: Presented in AAAI-15 Workshop: Beyond the Turing Tes

Implementation of Turing machines with the Scufl data-flow language

International audienceIn this paper, the expressiveness of the simple Scufl data-flow language is studied by showing how it can be used to implement Turing machines. To do that, several non trivial Scufl patterns such as self-looping or sub-workflows are required and we precisely explicit them. The main result of this work is to show how a complex workflow can be implemented using a very simple data-flow language. Beyond that, it shows that Scufl is a Turing complete language, given some restrictions that we discuss

On Completeness of Cost Metrics and Meta-Search Algorithms in \$-Calculus

In the paper we define three new complexity classes for Turing Machine undecidable problems inspired by the famous Cook/Levin's NP-complete complexity class for intractable problems. These are U-complete (Universal complete), D-complete (Diagonalization complete) and H-complete (Hypercomputation complete) classes. We started the population process of these new classes. We justify that some super-Turing models of computation, i.e., models going beyond Turing machines, are tremendously expressive and they allow to accept arbitrary languages over a given alphabet including those undecidable ones. We prove also that one of such super-Turing models of computation -- the \$-Calculus, designed as a tool for automatic problem solving and automatic programming, has also such tremendous expressiveness. We investigate also completeness of cost metrics and meta-search algorithms in \$-calculus

The Turing test as interactive proof

In 1950, Alan Turing proposed his eponymous test based on indistinguishability of verbal behavior as a replacement for the question "Can machines think?" Since then, two mutually contradictory but well-founded attitudes towards the Turing Test have arisen in the philosophical literature. On the one hand is the attitude that has become philosophical conventional wisdom, viz., that the Turing Test is hopelessly flawed as a sufficient condition for intelligence, while on the other hand is the overwhelming sense that were a machine to pass a real live full-fledged Turing Test, it would be a sign of nothing but our orneriness to deny it the attribution of intelligence. The arguments against the sufficiency of the Turing Test for determining intelligence rely on showing that some extra conditions are logically necessary for intelligence beyond the behavioral properties exhibited by an agent under a Turing Test. Therefore, it cannot follow logically from passing a Turing Test that the agent is intelligent. I argue that these extra conditions can be revealed by the Turing Test, so long as we allow a very slight weakening of the criterion from one of logical proof to one of statistical proof under weak realizability assumptions. The argument depends on the notion of interactive proof developed in theoretical computer science, along with some simple physical facts that constrain the information capacity of agents. Crucially, the weakening is so slight as to make no conceivable difference from a practical standpoint. Thus, the Gordian knot between the two opposing views of the sufficiency of the Turing Test can be cut.Engineering and Applied Science