Seminar of the Extension of the Mathematical Institute SAS in Košice
| next: | |
| 12. 3. 2026, 9:15 | Jozef Pócs |
| previous: | |
| 8. 1. 2026 | Simon Dieck (Delft University of Technology) – Automata learning algorithms obtained from Myhill-Nerode-style theorems |
| link to slides | |
| 22. 1. 2026 | Irena Jadlovská – A note on solving 3D discrete weakly delayed systems |
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Abstract:
We discuss the effective application of Putzer’s algorithm to the solution of three-dimensional discrete weakly delayed (WD) systems,
as defined in [1]. In particular, we show how the powers of the augmented $(3m+1)\times(3m+1)$ matrix $\mathcal A$
can be computed through a simple recursion involving only $3\times3$ matrices.
[1] Diblík, Josef, et al. "General solutions of weakly delayed discrete systems in 3D." Advances in Nonlinear Analysis 14.1 (2025): 20250121. |
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| 12. 2. 2026 | Galina Jirásková – The boundary of free convex languages |
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Abstract: We present a complete solution of the problem of finding
the deterministic state complexity of the boundary operation on the classes of
prefix-free, suffix-free, bifix-free, factor-free, and subword-free languages.
link to photo with the solution |
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| 26. 2. 2026 | Miroslav Repický – Combinatorial properties of ideals |
| Abstract: We deal with the cardinal characteristics $\mathrm{cov}^*(\mathcal{I})$ for the ideal $\mathcal{Z}$ of zero-density sets, the summable ideal $\mathcal{I}_{1/n}$, and for the generalizations $\mathcal{I}(\bar I)$ and $\mathcal{S}(\bar I)$ of these ideals dependent on an interval partition $\bar I$ of the set of natural numbers. We have characterizations of the inclusions $\mathcal{Z}(\bar I)\subseteq\mathcal{Z}$, $\mathcal{Z}(\bar I)\supseteq\mathcal{Z}$, $\mathcal{S}(\bar I)\subseteq\mathcal{I}_{1/n}$, $\mathcal{S}(\bar I)\supseteq\mathcal{I}_{1/n}$ using simple properties of the partition $\bar I$, and we show that the relational structures related to the cardinal characteristics of $\mathrm{cov}^*(\mathcal{I})$ for these ideals have their equivalent expressions in the sense of Tukey-connections in the form of pseudo-localizations of functions. |
