Asymptotic Proportion of Hard Instances of the Halting Problem

Although the halting problem is undecidable, imperfect testers that fail on some instances are possible. Such instances are called hard for the tester. One variant of imperfect testers replies "I don't know" on hard instances, another variant fails to halt, and yet another replies incorrectly "yes" or "no". Also the halting problem has three variants: does a given program halt on the empty input, does a given program halt when given itself as its input, or does a given program halt on a given input. The failure rate of a tester for some size is the proportion of hard instances among all instances of that size. This publication investigates the behaviour of the failure rate as the size grows without limit. Earlier results are surveyed and new results are proven. Some of them use C++ on Linux as the computational model. It turns out that the behaviour is sensitive to the details of the programming language or computational model, but in many cases it is possible to prove that the proportion of hard instances does not vanish.Comment: 18 pages. The differences between this version and arXiv:1307.7066v1 are significant. They have been listed in the last paragraph of Section 1. Excluding layout, this arXiv version is essentially identical to the Acta Cybernetica versio

Comparison between the two definitions of AI

Two different definitions of the Artificial Intelligence concept have been proposed in papers [1] and [2]. The first definition is informal. It says that any program that is cleverer than a human being, is acknowledged as Artificial Intelligence. The second definition is formal because it avoids reference to the concept of human being. The readers of papers [1] and [2] might be left with the impression that both definitions are equivalent and the definition in [2] is simply a formal version of that in [1]. This paper will compare both definitions of Artificial Intelligence and, hopefully, will bring a better understanding of the concept.Comment: added four new section

The Annotation Game: On Turing (1950) on Computing, Machinery, and Intelligence

This quote/commented critique of Turing's classical paper suggests that Turing meant -- or should have meant -- the robotic version of the Turing Test (and not just the email version). Moreover, any dynamic system (that we design and understand) can be a candidate, not just a computational one. Turing also dismisses the other-minds problem and the mind/body problem too quickly. They are at the heart of both the problem he is addressing and the solution he is proposing

Exact Gap Computation for Code Coverage Metrics in ISO-C

Test generation and test data selection are difficult tasks for model based testing. Tests for a program can be meld to a test suite. A lot of research is done to quantify the quality and improve a test suite. Code coverage metrics estimate the quality of a test suite. This quality is fine, if the code coverage value is high or 100%. Unfortunately it might be impossible to achieve 100% code coverage because of dead code for example. There is a gap between the feasible and theoretical maximal possible code coverage value. Our review of the research indicates, none of current research is concerned with exact gap computation. This paper presents a framework to compute such gaps exactly in an ISO-C compatible semantic and similar languages. We describe an efficient approximation of the gap in all the other cases. Thus, a tester can decide if more tests might be able or necessary to achieve better coverage.Comment: In Proceedings MBT 2012, arXiv:1202.582

First Person Singular: A review of Brian Rotman's "Becoming Beside Ourselves: Alphabet, ghosts, distributed human beings"

Brian Rotman argues that (one) “mind” and (one) “god” are only conceivable, literally, because of (alphabetic) literacy, which allowed us to designate each of these ghosts as an incorporeal, speaker-independent “I” (or, in the case of infinity, a notional agent that goes on counting forever). I argue that to have a mind is to have the capacity to feel. No one can be sure which organisms feel, hence have minds, but it seems likely that one-celled organisms and plants do not, whereas animals do. So minds originated before humans and before language --hence, a fortiori, before writing, whether alphabetic or ideographic