Computing Embeddings of Directed Bigraphs

Abstract

Directed bigraphs are a meta-model which generalises Milner's bigraphs by taking into account the request flow between controls and names. A key problem about these bigraphs is that of bigraph embedding, i.e., finding the embeddings of a bigraph inside a larger one. We present an algorithm for computing embeddings of directed bigraphs, via a reduction to a constraint satisfaction problem. We prove soundness and completeness of this algorithm, and provide an implementation in jLibBig, a general Java library for manipulating bigraphical reactive systems, together with some experimental results.

BiGGer: A Model Transformation Tool written in Java for Bigraph Rewriting in GrGen.NET

“…There are few practical solutions concerned with the bigraph matching problem for various kinds of bigraphs; a non-exhaustive presentation is the following. For binding bigraphs (i.e., links have local scopes) by an inductive characterization of matching (Birkedal et al, 2007;Damgaard et al, 2013); for directed bigraphs (which subsume pure bigraphs) (Bacci et al, 2009); for bigraphs with sharing (i.e., the place graph is a directed acyclic graph) by using a SAT-based algorithm (Sevegnani & Calder, 2016); for the pure case by (Miculan & Peressotti, 2014) as a CSP, and further an adapted reduction of the problem for directed bigraphs to a CSP (Chiapperini et al, 2020); and the work in Gassara et al (2019), which proposes a toolchain for bigraph matching that is conceptually most similar to our approach but not actively developed anymore and not as efficient as GrGen.NET.…”

Computing (optimal) embeddings of directed bigraphs

“…Edges of the first sub-network are described by the variables in (2) and their capacity is bounded by the number of points linked by the host handle since this is the maximum acceptable flux and corresponds to the case where each point passes through the same hyper-edge of the guest link graph. Edges of the second sub-network are described by the variables in (4) and, like the first group of links, have their capacity limited to 1; to be precise, some of these variables will never assume a value different from 0 because guest points can receive flux from anything but the host ports (as expressed by constraint (10)). Edges for the link structure of the guest are presented implicitly in the flux preservation constraints (see constraint (8)).…”

“…upward inner names) would not match with an entity of the agent and (those points) would be deleted anyway when composing the resulting agent back. Constraints (10), (19) and (20) disable edges between guest ports and host inner names, between mismatching ports of matching nodes and between ports of mismatching nodes. Constraint (22) ensures that ascending inner names or descending outer names of the redex are not matched with positive…”

“…The main differences with the conference version of the current work [10,11] are a substantial expansion of Section 2 with several examples and discussion, of Section 5 with more detailed examples, and the addition of the new Sections 6 and 7 about weighted directed bigraphs.…”