In this paper we address the chip-firing halting problem for undirected multigraphs. We give a polynomial algorithm for deciding the halting problem in the special case when the number of chips in the distribution is equal to the sum of the edge multiplicities of the graph. The key part of our algorithm uses convex cost flow optimization to give an efficient algorithmic proof of a theorem of An...

This paper studies the Turing degrees of various properties defined for universal numberings, that is, for numberings which list all partial-recursive functions. In particular properties relating to the domain of the corresponding functions are investigated like the set DEQ of all pairs of indices of functions with the same domain, the set DMIN of all minimal indices of sets and DMIN∗ of all in...

Since many real-world problems arising in the fields of compiler optimisation, automated software engineering, formal proof systems, and so forth are equivalent to the Halting Problem—the most notorious undecidable problem—there is a growing interest, not only academically, in understanding the problem better and in providing alternative solutions. Halting computations can be recognised by simp...

Since many real-world problems arising in the fields of compiler optimisation, automatised software engineering, formal proof systems, and so forth are equivalent to the Halting Problem—the most notorious undecidable problem—there is a growing interest, not only academically, in understanding the problem better and in providing alternative solutions. Halting computations can be recognised by si...

As early as 1783, the almost forgotten philosopher, metaphysicist, and psychologist Ferdinand Ueberwasser (1752– 1812) designated himself “Professor für empirische Psychologie und Logik” (professor of empirical psychology and logic) at the University of Münster, Germany. His position was initiated and supported by the minister and educational reformer Franz von Fürstenberg (1729–1810), who cons...

This document discusses the concept of an algorithm designed to locate the optimal solution to a problem in a (presumably) very large solution space. The algorithm attempts to locate the optimal solution to the problem by beginning a search at an arbitrary point in the solution space and then searching in the “local” area around the start point to find better solutions. The algorithm completes ...

We give a new proof of the following result (originally due to Linial and Post): it is undecidable whether a given calculus, that is a finite set of propositional formulas together with the rules of modus ponens and substitution, axiomatizes the classical logic. Moreover, we prove the same for every superintuitionistic calculus. As a corollary, it is undecidable whether a given calculus is cons...