Quantifying the Similarity of Non-bisimilar Labelled Transition Systems

Abstract

Equivalence checking is an established technique for automatically verifying that two behavioural models (Labelled Transition Systems, LTSs) are equivalent from the point of view of an external observer. When these models are not equivalent, the checker returns a Boolean result with a counterexample, which is a sequence of actions leading to a state where the equivalence relation is not satisfied. However, this counterexample does not give any indication of how far the two LTSs are one from another. One can wonder whether they are almost identical or totally different, which is quite different from a design or debugging point of view. In this paper, we present an approach for measuring the similarity between two LTS models. The set of metrics is computed automatically using a tool we implemented. Beyond presenting the foundations of the proposed solution, we will show how it can be applied to a concrete application domain for supporting the construction of IoT applications by composition of existing devices.

Consistent Substitution of Object in Rule-based IoT Applications

“…The mapping computation works in several steps. Given the behavioural models (LTSs) of two objects (former and new object), we first compute the similarity matrix between the two LTSs (using the DLTS tool [9]). Then, we use this matrix to build couples of states with the highest similarity value in the matrix.…”

“…Similarity measure. The first step relies on a comparison of both LTSs using a similarity measure [9] relying on bisimulation. This check first identifies bisimilar and non-bisimilar states.…”

“…Figure 6 overviews the tools supporting the computation of our solutions for object substitution. Note that some steps rely on existing tools (CADP [10], DLTS [9]) and other steps are automated by tools we implemented for this work in Python. Let us now comment on this picture to explain all the steps of our tool support.…”