POPL '77 Proceedings of the 4th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Deriving Bisimulation Congruences for Reactive Systems
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
Theoretical Computer Science - Special issue: Computational systems biology
Electronic Notes in Theoretical Computer Science (ENTCS)
Abstracting the Differential Semantics of Rule-Based Models: Exact and Automated Model Reduction
LICS '10 Proceedings of the 2010 25th Annual IEEE Symposium on Logic in Computer Science
Symmetry-Based model reduction for approximate stochastic analysis
CMSB'12 Proceedings of the 10th international conference on Computational Methods in Systems Biology
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Molecular biological models usually suffer from a large combinatorial explosion. Indeed, proteins form complexes and modify each others, which leads to the formation of a huge number of distinct chemical species (i.e. non-isomorphic connected components of proteins). Thus we cannot generate explicitly the quantitative semantics of these models, and even less compute their properties. In this paper we propose a formal framework to automatically reduce the combinatorial complexity of the differential semantics of rule-based models. Our reduction is based on two abstractions, which are combined thanks to a generic product. The first abstraction tracks the flow of information between the different regions of chemical species, so as to detect and abstract away some useless correlations between the state of sites. The second abstraction detects pairs of sites having the same capabilities of interaction, and abstracts away any distinction between them. The initial semantics and the reduce one are formally related by Abstract Interpretation.