The main topic of the present work is the relation that a set X is strongly hyperimmune-free relative to Y . Here X is strongly hyperimmune-free relative to Y if and only if for every partial X-recursive function p there is a partial Y -recursive function q such that every a in the domain of p is also in the domain of q and satisfies p(a) < p(a), that is, p is majorised by q. For X being hyperi...

The programming approach to computability presented in the textbook by Kfoury, Moll, and Arbib in 1982 has been embedded into a programming course following the textbook by Abelson and Sussman. This leads to a course concept teaching good programming practice and clear theoretical concepts simultaneously. Here, we explain some of the main points of this approach: the halting problem, primitive ...

Modern distributed applications require coallocation of massive amounts of resources. Grid level allocation systems must efficiently decide where these applications can be executed. To this end, the resource requests are described as labeled graphs, which must be matched with equivalent labeled graphs of available resources. The coallocation problem described in the paper has real-world require...

Concerns of users about the privacy of their data are becoming more important to providers of online services, as they develop into a major barrier for broad acceptance of applications, that gather data about their users. With P3P there exists a standard that, in the context of web-based applications, gives users some control over the gathering, use and relaying of their data. However, P3P stil...

This paper reviews and investigates Bennett s notions of strong and weak computational depth also called logical depth for in nite binary sequences Roughly an in nite binary sequence x is de ned to be weakly useful if every element of a non negligible set of decidable sequences is reducible to x in recursively bounded time It is shown that every weakly useful sequence is strongly deep This resu...

There are a number of questions regarding the size of programs for calculating natural numbers, sequences, sets, and functions, which are best answered by considering computations in which one is allowed to consult an oracle for the halting problem. Questions of this kind suggested by work of T. Kamae and D. W. Loveland are treated.

P 6= NP ⇔ SAT 6∈ P . We propose this to be true because the satisfiability problem for propositional logic formulas (SAT) is the Halting Problem [Turing, 1937] in disguise and therefore undecidable. Since the input space is finite, however, SAT can still be solved by simulating no less than all possible, that is exponentially many, configurations. In a nutshell, the halting portion of a program...

In general relativity the gravitational field is encoded in the Riemannian geometry of space-time. Much of the conceptual compactness and mathematical elegance of the theory can be traced back to this central idea. The encoding is also directly responsible for the most dramatic ramifications of the theory: the big-bang, black holes and gravitational waves. However, it also leads one to the conc...

In this article, a program block without halting instructions is called No-StopCode program block. If a program consists of two blocks, where the first block is parahalting (i.e. halt for all states) and No-StopCode, and the second block is parahalting and shiftable, it can be computed by combining the computation results of the two blocks. For a program which consists of a instruction and a bl...