Complexity of Road Coloring with Prescribed Reset Words

By the Road Coloring Theorem (Trahtman, 2008), the edges of any aperiodic directed multigraph with a constant out-degree can be colored such that the resulting automaton admits a reset word. There may also be a need for a particular reset word to be admitted. For certain words it is NP-complete to decide whether there is a suitable coloring of a given multigraph. We present a classification of all words over the binary alphabet that separates such words from those that make the problem solvable in polynomial time. We show that the classification becomes different if we consider only strongly connected multigraphs. In this restricted setting the classification remains incomplete.Comment: To be presented at LATA 201

Documentation of landslides and inaccessible parts of a mine using an unmanned uav system and methods of digital terrestrial photogrammetry

Quite a big boom has recently been experienced in the technology of unmanned aerial vehicles (UAV). In conjunction with dense matching system, it gives one a powerful tool for the creation of digital terrain models and orthophotomaps. This system was used for the documentation of landslides and inaccessible parts of the Nástup Tušimice mine in the North Bohemian Brown Coal Basin (Czech Republic). The images were taken by the GATEWING X100 unmanned system that automatically executed photo flights an area of interest. For detailed documentation of selected parts of the mine, we used the method of digital terrestrial photogrammetry. The main objective was to find a suitable measurement technology for operational targeting of landslides and inaccessible parts of the mine, in order to prepare the basics for remediation work

Experiments on synchronizing automata

This work is motivated by the Černý Conjecture – an old unsolved problem in the automata theory. We describe the results of the experiments on synchronizing automata, which have led us to two interesting results. The first one is that the size of an automaton alphabet may play an important role in the issue of synchronization: we have found a 5-state automaton over a 3-letter alphabet which attains the upper bound from the Černý Conjecture, while there is no such automaton (except Černý automaton $C_5$) over a binary alphabet. The second result emerging from the experiments is a theorem describing the dependencies between the automaton structure $S$ expressed in terms of the so-called merging system and the maximal length of all minimal synchronizing words for automata of type $S$

Body Size of Wood Ant Workers Affects their Work Division

The division of functions among ant workers and their mutual cooperation is one of the reasons for ants’ success. The activities that workers perform in the nest can be divided by age or morphology. We studied the body size of workers of the wood ant Formica polyctena as a function of their activity. Our results show that workers exploiting protein baits were larger than workers attracted to carbohydrate baits. The biggest of all were workers located at the upper parts of the nest, which shows the importance of nest defense and maintenance. It also points that the distribution of functions does not have to be given only by workers age. Work division based on several mechanisms may be advantageous for colony functioning