Vojtěch Vorel
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View article: Lower Bounds on Avoiding Thresholds
Lower Bounds on Avoiding Thresholds Open
For a DFA, a word avoids a subset of states, if after reading that word the automaton cannot be in any state from the subset regardless of its initial state. A subset that admits an avoiding word is avoidable. The k-avoiding threshold of a…
View article: A new Lower Bound for Reset Threshold of Binary Synchronizing Automata with Sink
A new Lower Bound for Reset Threshold of Binary Synchronizing Automata with Sink Open
We present a new series of examples of binary slowly synchronizing automata with a sink state. The reset threshold of the $n$-state automaton in this series is $\frac{n^2}{4}+2n-9$. This improves on the previously known lower bound for the…
View article: On Basic Properties of Jumping Finite Automata
On Basic Properties of Jumping Finite Automata Open
We complete the initial study of jumping finite automata, which was started in a former article of Meduna and Zemek [7]. The open questions about basic closure properties are solved. Besides this, we correct erroneous results presented in …
View article: Subset Synchronization and Careful Synchronization of Binary Finite Automata
Subset Synchronization and Careful Synchronization of Binary Finite Automata Open
We present a strongly exponential lower bound that applies both to the subset synchronization threshold for binary deterministic automata and to the careful synchronization threshold for binary partial automata. In the later form, the resu…