Strategies as sheaves and interactive equivalences for CCS
Résumé
Joyal, Nielsen and Winskel have proposed to interpret concurrent processes as presheaves over categories of observations. We propose a new category of observations for Milner's Calculus of Communicating Systems (CCS), which we equip with a Grothendieck topology. We propose to consider as a model for CCS processes not merely presheaves, but sheaves on this category. This model altogether forms a stack (a weak form of sheaf), which yields an intrinsic notion of interaction by amalgamation. In this setting, and mimicking observational equivalences, we then define a notion of interactive equivalence for processes. We consider two instances, the respective analogues of must and fair testing in CCS (De Nicola and Hennessy), and show that they coincide.
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