Gravitational search algorithm (GSA) is one of the newest swarm based optimization algorithms, which has been inspired by the Newtonian laws of gravity and motion. GSA has empirically shown to be an efficient and robust stochastic search algorithm. Since introducing GSA a convergence analysis of this algorithm has not yet been developed. This paper introduces the first attempt to a formal conve...

Gravitational search algorithm (GSA) is one of the newest swarm based optimization algorithms, which has been inspired by the Newtonian laws of gravity and motion. GSA has empirically shown to be an efficient and robust stochastic search algorithm. Since introducing GSA a convergence analysis of this algorithm has not yet been developed. This paper introduces the first attempt to a formal conve...

We provide a formal proof within First Order Relativity Theory that no observer can travel faster than the speed of light. Originally reported by Stannett and Németi [1].

Suppose two judges each classify a group of objects into one of several nominal categories. It has been observed in the literature that, for fixed observed agreement between the judges, Cohen’s kappa penalizes judges with similar marginals compared to judges who produce different marginals. This paper presents a formal proof of this phenomenon.

In this paper, we show that any proof of the Collatz 3n + 1 Conjecture must have an infinite number of lines. Therefore, no formal proof is possible. We also discuss whether the proof strategy in this paper has any promise for proving that the Riemann Hypothesis is also unprovable.

We show that with a simple translation for normal programs, we can use the pstable model semantics to get the stable models of a normal program. We present the formal proof of this statement.

This note collects the formal proof sketches that I have done. 1 Algebra: Irrationality of √ 2

We extend the Multi-lane Spatial Logic MLSL, introduced in previous work for proving the safety (collision freedom) of traffic maneuvers on a multi-lane highway, by length measurement and dynamic modalities. We investigate the proof theory of this extension, called EMLSL. To this end, we prove the undecidability of EMLSL but nevertheless present a sound proof system which allows for reasoning a...