Minimization and equivalence in multi-valued logical models of regulatory networks
Multi-valued logical models can be used to describe biological networks on a high level of abstraction based on the network structure and logical parameters capturing regulatory effects. Interestingly, the dynamics of two distinct models need not necessarily be different, which might hint at either only non-functional characteristics distinguishing the models or at different possible implementations for the same behaviour. Here, we study the conditions allowing for such effects by analysing classes of dynamically equivalent models and both structurally maximal and minimal representatives of such classes. Finally, we present an efficient algorithm that constructs a minimal representative of the respective class of a given multi-valued model.
KeywordsRegulatory networks Multi-valued models Minimization Equivalence Transition system
- Gallet E, Manceny M, Le Gall P, Ballarini P (2014) An LTL model checking approach for biological parameter inference. In: Merz S, Pang J (eds) Formal methods and software engineering, lecture notes in computer science, vol 8829, Springer International Publishing, pp 155–170Google Scholar
- Gershenson C (2004) Introduction to random Boolean networks. arXiv:nlin/0408006
- Siebert H (2008) Local structure and behavior of Boolean bioregulatory networks. In: Horimoto K, Regensburger G, Rosenkranz M, Yoshida H (eds) Algebraic biology, lecture notes in computer science, vol 5147, Springer, Heidelberg, pp 185–199Google Scholar
- Streck A, Siebert H (2014) Equivalences in multi-valued asynchronous models of regulatory networks. In: Wąs J, Sirakoulis GC, Bandini S (eds) Cellular automata, lecture notes in computer science, vol 8751, Springer International Publishing, pp 571–575Google Scholar