# How to Kill Epsilons with a Dagger

Abstract : We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or $ϵ$-transitions. Our approach employs monads with a parametrized fixpoint operator $†$ to give a semantics to those systems and implement a sound procedure of abstraction of the internal transitions, whose labels are seen as the unit of a free monoid. More broadly, our approach extends the standard coalgebraic framework for state-based systems by taking into account the algebraic structure of the labels of their transitions. This allows to consider a wide range of other examples, including Mazurkiewicz traces for concurrent systems.
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Cited literature [23 references]

https://hal.inria.fr/hal-01408752
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### Citation

Filippo Bonchi, Stefan Milius, Alexandra Silva, Fabio Zanasi. How to Kill Epsilons with a Dagger. 12th International Workshop on Coalgebraic Methods in Computer Science (CMCS), Apr 2014, Grenoble, France. pp.53-74, ⟨10.1007/978-3-662-44124-4_4⟩. ⟨hal-01408752⟩

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