A Behavioral Congruence for Concurrent Constraint Programming with Nondeterministic Choice

Concurrent constraint programming (ccp) is a well-established model of concurrency for reasoning about systems of multiple agents that interact with each other by posting and querying partial information on a shared space. (Weak) bisimilarity is one of the most representative notions of behavioral equivalence for models of concurrency. A notion of weak bisimilarity, called weak saturated bisimilarity (\(\dot{\approx}_{sb}\)), was recently proposed for ccp. This equivalence improves on previous bisimilarity notions for ccp that were too discriminating and it is a congruence for the choice-free fragment of ccp. In this paper, however, we show that \(\dot{\approx}_{sb}\) is not a congruence for ccp with nondeterministic choice. We then introduce a new notion of bisimilarity, called weak full bisimilarity (≈ f ), and show that it is a congruence for the full language of ccp. We also show the adequacy of ≈ f by establishing that it coincides with the congruence induced by closing \(\dot{\approx}_{sb}\) under all contexts. The advantage of the new definition is that, unlike the congruence induced by \(\dot{\approx}_{sb}\), it does not require quantifying over infinitely many contexts.