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In [1], we introduced the weakly synchronizing languages for probabilistic automata. In this report, we show that the emptiness problem of weakly synchronizing languages for probabilistic automata is undecidable. This implies that the decidability result of [1-3] for the emptiness problem of weakly synchronizing language is incorrect.
We study the problems of finding a shortest synchronizing word and its length for a given prefix code. This is done in two different settings: when the code is defined by an arbitrary decoder recognizing its star and when the code is defined by its l
Instead of looking at the lengths of synchronizing words as in v{C}ernys conjecture, we look at the switch count of such words, that is, we only count the switches from one letter to another. Where the synchronizing words of the v{C}erny automata $ma
It was conjectured by v{C}erny in 1964, that a synchronizing DFA on $n$ states always has a synchronizing word of length at most $(n-1)^2$, and he gave a sequence of DFAs for which this bound is reached. Until now a full analysis of all DFAs reaching
The probabilistic bisimilarity distance of Deng et al. has been proposed as a robust quantitative generalization of Segala and Lynchs probabilistic bisimilarity for probabilistic automata. In this paper, we present a characterization of the bisimilar
We present an infinite series of $n$-state Eulerian automata whose reset words have length at least $(n^2-3)/2$. This improves the current lower bound on the length of shortest reset words in Eulerian automata. We conjecture that $(n^2-3)/2$ also for