Borrowed Contexts for Attributed Graphs

Abstract

Abstract. Borrowed context graph transformation is a simple and powerful technique developed by Ehrig and König that allow us to derive labeled transitions and bisimulation congruences for graph transformation systems or, in general, for process calculi that can be defined in terms of graph transformation systems. Moreover, the same authors have also shown how to use this technique for the verification of bisimilarity. In principle, the main results about borrowed context transformation do not apply only to plain graphs, but they are generic in the sense that they apply to all categories that satisfy certain properties related to the notion of adhesivity. In particular, this is the case of attributed graphs. However, as we show in the paper, the techniques used for checking bisimilarity are not equally generic and, in particular they fail, if we want to apply them to attributed graphs. To solve this problem, in this paper, we define a special notion of symbolic graph bisimulation and show how it can be used to check bisimilarity of attributed graphs.

Checking Bisimilarity for Attributed Graph Transformation

“…However, in [14] we also proved that the following notion of S-bisimilarity over symbolic graphs could be used for proving bisimilarity of attributed graphs.…”

“…So that for deciding if two attributed graphs are bisimilar we could check if their associated grounded graphs are bisimilar in the category of symbolic graphs. Unfortunately, in [14] we proved that two attributed graphs may be bisimilar as attributed graphs, while their associated grounded symbolic graphs are not bisimilar as symbolic graphs.…”

“…The key issue is that, using symbolic graphs, we can decouple the proof of properties about the graph structure of the given graphs from the proof of properties of data and computations, in a similar way that constraint logic programming [11] decouples computation or constraint solving from deduction. The paper builds on [14], where we showed that bisimilarity of attributed graphs is in a way equivalent to a relation, which we call s-bisimilarity, of symbolic graphs. However, in [14] it was unclear how we could use those results to define techniques to check bisimilarity, since the notion of s-bisimilarity is somewhat involved.…”

“…The paper builds on [14], where we showed that bisimilarity of attributed graphs is in a way equivalent to a relation, which we call s-bisimilarity, of symbolic graphs. However, in [14] it was unclear how we could use those results to define techniques to check bisimilarity, since the notion of s-bisimilarity is somewhat involved.…”

“…In sections 2 and 3, we introduce borrowed context transformation and attributed and symbolic graphs. In section 4, we recall the main results from [14]. Sections 5 and 6 are devoted to present the inference system and the tableau method.…”