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**5**

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**1**answer

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### Is it decidable whether the support of a rational $\mathbb{Z}$-series is a regular language?

Let $S \in \mathbb{Z}\langle\langle A\rangle\rangle$ be a rational series in noncommutative variables. The support of $S$ is the set of all words $u \in A^*$ such that $(S, u) \not= 0$. It is ...

**3**

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**3**answers

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### Finite variation and idempotent languages and automata.

Let $L$ be a regular language over alphabet $\Sigma$ and let $A:=(Q,\Sigma,\delta, q_0, F)$ be the minimal DFA recognizing $L$. For every $w\in \Sigma^*$ define the variation of $w$ w.r.t. $L$ by
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