Often, it is argued that some problems in data-flow analysis such as e.g. worst case execution time analysis are undecidable (because the halting problem is) and therefore only a conservative approximation of the desired information is possible. In this paper, we show that the semantics for some important real programming languages – in particular those used for programming embedded devices – c...

Accelerating Turing machines are abstract devices that have the same computational structure as Turing machines, but can perform super-tasks. I argue that performing super-tasks alone does not buy more computational power, and that accelerating Turing machines do not solve the halting problem. To show this, I analyze the reasoning that leads to Thomson's paradox, point out that the paradox rest...

In the BSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post’s Problem over the reals significantly differs from its classical, discrete variant where advanced diagonalization techniques are only known to yield the existence of such i...

A reduction system for regular expressions is presented. For a regular expression t, the reduction system is proved to terminate in a state where the most-reduced expression readily yields a semi-linear representation for the Parikh image of the language of t.

The goal of this comment is to first point out two loopholes in the paper by Li et al. (2006): 1) so-designed efficient maximal margin criterion (MMC) algorithm for small sample size (SSS) problem is problematic and 2) the discussion on the equivalence with the null-space-based methods in SSS problem does not hold. Then, we will present a really efficient MMC algorithm for SSS problem.

Suppose that DoesHalt( Program, Input ) is a program that does its best to determine if Program halts on Input. It has the following property: if it returns true then Program halts on Input, if it returns false then Program does not halt on input. There may be some cases when it returns nothing, but whenever it is humanly possible to make a determination it will make it. And when it does make a...

In this paper we provide a survey of the technique that allows giving a simple proof that all Turing machines with two letters and two states have a decidable halting problem. The result was proved by L. Pavlot-skaya in 1973.

We use the minimal instruction set F-4 computer to define a minimal Turing complete T7 computer suitable for genetic programming (GP) and amenable to theoretical analysis. Experimental runs and mathematical analysis of the T7, show the fraction of halting programs is drops to zero as bigger programs are run.

A fractal model of the cosmos is presented in terms of distinct orders of universes, particles, substrates and strata. Each universe in the fractal cosmos is characterized by the radius of that universe divided by the effective radius of one of its stratum particles. It is shown that this size ratio increases rapidly for higher order universes and that a series of universes of descending order ...

We trace the emergence of unsolvable problems in algebra and topology from the unsolvable halting problem for Turing machines. §