Abstract: Rule-based modeling languages, as Kappa, allow for the description of very detailed mechanistic models. Yet, as the rules become more and more numerous, there is a need for formal methods to enhance the level of confidence in the models that are described with these languages. We develop abstract interpretation tools to capture invariants about the biochemical structure of bio-molecular species that may occur in a given model. In previous works, we have focused on the relationships between the states of the sites that belong to a same instance of a protein. This comes down to detect for a specific set of patterns, which ones may be reachable during the execution of the model. In this paper, we generalize this approach to a broader family of abstract domains, that we call orthogonal sets of patterns. More precisely, an orthogonal set of patterns is obtained by refining recursively the information about some patterns containing a given protein, so as to partition of the set of occurrences of this protein in any mixture.

@article{Feret201827,
title = "Reachability Analysis via Orthogonal Sets of Patterns ",
journal = "Electronic Notes in Theoretical Computer Science ",
volume = "335",
number = "",
pages = "27 - 48",
year = "2018",
note = "7th International Workshop on Static Analysis and Systems Biology (SASB 2016) ",
issn = "1571-0661",
doi = "https://doi.org/10.1016/j.entcs.2018.03.007",
url = "https://www.sciencedirect.com/science/article/pii/S1571066118300094",
author = "Jerome Feret and Kim Quy\^en L\'y",
keywords = "Rule-based models",
keywords = "Abstract interpretation",
keywords = "Reachability analysis "
}