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On quotients of Boolean control networks

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Document pages: 12 pages

Abstract: In this paper, we focus on the study of quotients of Boolean control networks(BCNs) with the motivation that they might serve as smaller models that stillcarry enough information about the original network. Given a BCN and anequivalence relation on the state set, we consider a labeled transition systemthat is generated by the BCN. The resulting quotient transition system thennaturally captures the quotient dynamics of the BCN concerned. We thereforedevelop a method for constructing a Boolean system that behaves equivalently tothe resulting quotient transition system. The use of the obtained quotientsystem for control design is discussed and we show that for BCNs, controllersynthesis can be done by first designing a controller for a quotient andsubsequently lifting it to the original model. We finally demonstrate theapplicability of the proposed techniques on a biological example.

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