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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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Regular Cost Functions, Part I: Logic and Algebra over Words

Thomas Colcombet.

The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to each input the two values "inside" and "outside". This theory&nbsp;[&hellip;]

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Controlling a random population

Thomas Colcombet ; Nathanaël Fijalkow ; Pierre Ohlmann.

Bertrand et al. introduced a model of parameterised systems, where each agent is represented by a finite state system, and studied the following control problem: for any number of agents, does there exist a controller able to bring all agents to a target state? They showed that the problem is&nbsp;[&hellip;]

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