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Logics with rigidly guarded data tests

Gabriele Puppis ; Thomas Colcombet ; Clemens Ley.

The notion of orbit finite data monoid was recently introduced by Bojanczyk as an algebraic object for defining recognizable languages of data words. Following Buchi's approach, we introduce a variant of monadic second-order logic with data equality tests that captures precisely the data languages&nbsp;[&hellip;]

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Transforming structures by set interpretations

Thomas Colcombet ; Christof Löding.

We consider a new kind of interpretation over relational structures: finite sets interpretations. Those interpretations are defined by weak monadic second-order (WMSO) formulas with free set variables. They transform a given structure into a structure with a domain consisting of finite sets of&nbsp;[&hellip;]

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Boundedness in languages of infinite words

Mikołaj Bojańczyk ; Thomas Colcombet.

We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions where two new variants of the Kleene star $L^*$ are&nbsp;[&hellip;]

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Playing Safe, Ten Years Later

Thomas Colcombet ; Nathanaël Fijalkow ; Florian Horn.

We consider two-player games over graphs and give tight bounds on the memory size of strategies ensuring safety objectives. More specifically, we show that the minimal number of memory states of a strategy ensuring a safety objective is given by the size of the maximal antichain of left quotients&nbsp;[&hellip;]

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