How to Kill Epsilons with a Dagger

Filippo Bonchi (1) , Stefan Milius (2) , Alexandra Silva (3, 4, 5) , Fabio Zanasi (1)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 FAU - Friedrich-Alexander Universität Erlangen-Nürnberg = University of Erlangen-Nuremberg
3 Radboud University [Nijmegen]
4 CWI - Centrum Wiskunde & Informatica
5 Universidade do Minho = University of Minho [Braga]

We propose an abstract framework for modeling state-based systems with internal behavior as e.g. given by silent or $\mathrm{ϵ<!--\; ϵ\; -->}$-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.

Domaines: Informatique [cs]

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⟩