2,162 research outputs found
On algorithm and robustness in a non-standard sense
In this paper, we investigate the invariance properties, i.e. robust- ness, of phenomena related to the notions of algorithm, finite procedure and explicit construction. First of all, we provide two examples of objects for which small changes completely change their (non)computational behavior. We then isolate robust phenomena in two disciplines related to computability
Heinrich Behmann's 1921 lecture on the decision problem and the algebra of logic
Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in
G\"ottingen in 1921 with a thesis on the decision problem. In his thesis, he
solved-independently of L\"owenheim and Skolem's earlier work-the decision
problem for monadic second-order logic in a framework that combined elements of
the algebra of logic and the newer axiomatic approach to logic then being
developed in G\"ottingen. In a talk given in 1921, he outlined this solution,
but also presented important programmatic remarks on the significance of the
decision problem and of decision procedures more generally. The text of this
talk as well as a partial English translation are included
Informatics: Science or Téchne?
Informatics is generally understood as a “new technology” and is therewith discussed according to technological aspects such as speed, data retrieval, information control and so on. Its widespread use from home appliances to enterprises and universities is not the result of a clear-cut analysis of its inner possibilities but is rather dependent on all sorts of ideological promises of unlimited progress. We will discuss the theoretical definition of informatics proposed in 1936 by Alan Turing in order to show that it should be taken as final and complete. This definition has no relation to the technology because Turing defines computers as doing the work of solving problems with numbers. This formal definition implies nonetheless a relation to the non-formalized elements around informatics, which we shall discuss through the Greek notion of téchne
Zeno machines and hypercomputation
This paper reviews the Church-Turing Thesis (or rather, theses) with
reference to their origin and application and considers some models of
"hypercomputation", concentrating on perhaps the most straight-forward option:
Zeno machines (Turing machines with accelerating clock). The halting problem is
briefly discussed in a general context and the suggestion that it is an
inevitable companion of any reasonable computational model is emphasised. It is
hinted that claims to have "broken the Turing barrier" could be toned down and
that the important and well-founded role of Turing computability in the
mathematical sciences stands unchallenged.Comment: 11 pages. First submitted in December 2004, substantially revised in
July and in November 2005. To appear in Theoretical Computer Scienc
- …