TY - JOUR

T1 - Observability of Boolean networks

T2 - A graph-theoretic approach

AU - Laschov, Dmitriy

AU - Margaliot, Michael

AU - Even, Guy

N1 - Funding Information:
The research of MM is supported in part by the ISF . The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor David Angeli under the direction of Editor Andrew R. Teel.

PY - 2013/8

Y1 - 2013/8

N2 - Boolean networks (BNs) are discrete-time dynamical systems with Boolean state-variables and outputs. BNs are recently attracting considerable interest as computational models for genetic and cellular networks. We consider the observability of BNs, that is, the possibility of uniquely determining the initial state given a time sequence of outputs. Our main result is that determining whether a BN is observable is NP-hard. This holds for both synchronous and asynchronous BNs. Thus, unless P = NP, there does not exist an algorithm with polynomial time complexity that solves the observability problem. We also give two simple algorithms, with exponential complexity, that solve this problem. Our results are based on combining the algebraic representation of BNs derived by D. Cheng with a graph-theoretic approach. Some of the theoretical results are applied to study the observability of a BN model of the mammalian cell cycle.

AB - Boolean networks (BNs) are discrete-time dynamical systems with Boolean state-variables and outputs. BNs are recently attracting considerable interest as computational models for genetic and cellular networks. We consider the observability of BNs, that is, the possibility of uniquely determining the initial state given a time sequence of outputs. Our main result is that determining whether a BN is observable is NP-hard. This holds for both synchronous and asynchronous BNs. Thus, unless P = NP, there does not exist an algorithm with polynomial time complexity that solves the observability problem. We also give two simple algorithms, with exponential complexity, that solve this problem. Our results are based on combining the algebraic representation of BNs derived by D. Cheng with a graph-theoretic approach. Some of the theoretical results are applied to study the observability of a BN model of the mammalian cell cycle.

KW - Boolean control networks

KW - Computational complexity

KW - Gene regulating networks

KW - Logical systems

KW - Observability

KW - Observable graphs

KW - Systems biology

UR - http://www.scopus.com/inward/record.url?scp=84882450040&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2013.04.038

DO - 10.1016/j.automatica.2013.04.038

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AN - SCOPUS:84882450040

SN - 0005-1098

VL - 49

SP - 2351

EP - 2362

JO - Automatica

JF - Automatica

IS - 8

ER -