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Multiwords are words in which a single symbol can be replaced by a nonempty set of symbols. They extend the notion of partial words. A word w is certain in a multiword M if it occurs in every word that can be obtained by selecting one single symbol among the symbols provided in each position of M. Motivated by a problem on incomplete databases, we investigate a variant of the pattern matching problem which is to decide whether a word w is certain in a multiword M. We study the language CERTAIN(w) of multiwords in which w is certain. We show that this regular language is aperiodic for three large families of words. We also show its aperiodicity in the case of partial words over an alphabet with at least three symbols.
We study hybrid systems with strong resets from the perspective of
formal language theory. We define a notion of hybrid regular
expression and prove a Kleene-like theorem for hybrid systems. We
also prove the closure of these systems under determinisation and
complementation. Finally, we prove that the reachability problem is
undecidable for synchronized products of hybrid systems.
We show that the inclusion problem is decidable for rational languages
of words indexed by scattered countable linear orderings. The method leans on a reduction to
the decidability of the monadic second order theory of the infinite binary tree
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