K metodice řešení hybridních obvodů grafy signálových toků
K3-Worm Colorings of Graphs: Lower Chromatic Number and Gaps in the Chromatic Spectrum
A K3-WORM coloring of a graph G is an assignment of colors to the vertices in such a way that the vertices of each K3-subgraph of G get precisely two colors. We study graphs G which admit at least one such coloring. We disprove a conjecture of Goddard et al. [Congr. Numer. 219 (2014) 161-173] by proving that for every integer k ≥ 3 there exists a K3-WORM-colorable graph in which the minimum number of colors is exactly k. There also exist K3-WORM colorable graphs which have a K3-WORM coloring with...
Karp-Miller trees for a branching extension of VASS.
k-counting automata
In this paper, we define k-counting automata as recognizers for ω-languages, i.e. languages of infinite words. We prove that the class of ω-languages they recognize is a proper extension of the ω-regular languages. In addition we prove that languages recognized by k-counting automata are closed under Boolean operations. It remains an open problem whether or not emptiness is decidable for k-counting automata. However, we conjecture strongly that it is decidable and give formal reasons why we believe...
k-counting automata
In this paper, we define k-counting automata as recognizers for ω-languages, i.e. languages of infinite words. We prove that the class of ω-languages they recognize is a proper extension of the ω-regular languages. In addition we prove that languages recognized by k-counting automata are closed under Boolean operations. It remains an open problem whether or not emptiness is decidable for k-counting automata. However, we conjecture strongly...
Kolmogorov complexity and probability measures
Classes of strings (infinite sequences resp.) with a specific flow of Kolmogorov complexity are introduced. Namely, lower bounds of Kolmogorov complexity are prescribed to strings (initial segments of infinite sequences resp.) of specified lengths. Dependence of probabilities of the classes on lower bounds of Kolmogorov complexity is the main theme of the paper. Conditions are found under which the probabilities of the classes of the strings are close to one. Similarly, conditions are derived under...
Kolmogorov complexity, pseudorandom generators and statistical models testing
An attempt to formalize heuristic concepts like strings (sequences resp.) “typical” for a probability measure is stated in the paper. Both generating and testing of such strings is considered. Kolmogorov complexity theory is used as a tool. Classes of strings “typical” for a given probability measure are introduced. It is shown that no pseudorandom generator can produce long strings from the classes. The time complexity of pseudorandom generators with oracles capable to recognize “typical” strings...
Kombinatorika, zložitosť a náhodnost
Komplexität von Algorithmen mit Anwendung auf die Analysis.