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A non-regular language of infinite trees that is recognizable by a sort-wise finite algebra

Mikołaj Bojańczyk ; Bartek Klin.

$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is regular if and only if it is recognized by an algebra that is&nbsp;[&hellip;]

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Optimizing tree decompositions in MSO

Mikołaj Bojańczyk ; Michał Pilipczuk.

The classic algorithm of Bodlaender and Kloks [J. Algorithms, 1996] solves the following problem in linear fixed-parameter time: given a tree decomposition of a graph of (possibly suboptimal) width k, compute an optimum-width tree decomposition of the graph. In this work, we prove that this problem&nbsp;[&hellip;]

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