On Density in Coordination Languages

On Distributed Density in Tuple-based Coordination Languages

“…This paper fits into the continuity of previous work done by the authors, among others of [5,8,9,12,16]. As a result, our approach follows the same lines of research, and employs de boer and Palamidessi's modular embedding to test the expressiveness of languages.…”

“…We have essentially followed the same lines and in particular have used de Boer and Palamidessi's notion of modular embedding to compare the families of sublanguages of Dense Bach and Dense Bach with Distributed Density. Accordingly, we have established a gain of expressivity, namely that Dense Bach with Distributed Density is strictly more expressive than Dense Bach and, consequently, in view of the results of [12], strictly more expressive than the Bach and Linda languages.…”

“…The proof proceeds similarly in the case u j = b k for some k by then considering tell ([b](1)); AB and tell([b](1)); (AB + ask ([b](1))). (iii) Otherwise, L DB (nask,tell) would be embedded in L DB (get,tell), which has been prooved impossible in proposition 12(iv) of [12]. (iv) Otherwise, L DB (ask,tell) would be embedded in L DBD (nask,tell) which contradicts proposition 6(ii).…”

On Multiplicities in Tuple-Based Coordination Languages: The Bach Family of Languages and Its Expressiveness Study

“…Following Linda, it permits to model in an elegant way the interaction between different components through the deposit and retrieval of tuples in a shared space. As its basic form only allows the manipulation of one tuple at a time and since the selection between several tuples matching a required one is provided in a non-deterministic fashion, a first extension was proposed in [22] in the aim of enriching traditional data-based coordination languages by a notion of multiplicity (historically named density) attached to tuples, thereby yielding a new coordination language, called Dense Bach. In a second extension we have proposed in [18] to consider lists of tuples among which densities are distributed.…”

“…Introducing variants of languages necessarily calls for a gain of expressiveness. Based on previous work by the authors, among others of [8,12,14,18,22,29], we shall employ de Boer and Palamidessi's modular embedding and show that Bach is less expressive than Dense Bach, which itself is less expressive than VD-Bach. VD-Bach being similar in essence to multiset rewriting, as introduced in Gamma [1,2], we shall also compare the two languages and prove that Gamma is actually more expressive than VD-Bach.…”