Towards Trace Metrics via Functor Lifting

Paolo Baldan, Filippo Bonchi, Henning Kerstan, Barbara König, Marc Herbstritt
2015 Conference on Algebra and Coalgebra in Computer Science  
We investigate the possibility of deriving metric trace semantics in a coalgebraic framework. First, we generalize a technique for systematically lifting functors from the category Set of sets to the category PMet of pseudometric spaces, by identifying conditions under which also natural transformations, monads and distributive laws can be lifted. By exploiting some recent work on an abstract determinization, these results enable the derivation of trace metrics starting from coalgebras in Set.
more » ... ore precisely, for a coalgebra in Set we determinize it, thus obtaining a coalgebra in the Eilenberg-Moore category of a monad. When the monad can be lifted to PMet, we can equip the final coalgebra with a behavioral distance. The trace distance between two states of the original coalgebra is the distance between their images in the determinized coalgebra through the unit of the monad. We show how our framework applies to nondeterministic automata and probabilistic automata.
doi:10.4230/lipics.calco.2015.35 dblp:conf/calco/BaldanBK015 fatcat:q737653gurd3lnw7go6u5uuzie