TY - JOUR

T1 - A Polynomial-Time Algorithm for Solving the Minimal Observability Problem in Conjunctive Boolean Networks

AU - Weiss, Eyal

AU - Margaliot, Michael

N1 - Publisher Copyright:
© 1963-2012 IEEE.

PY - 2019/7

Y1 - 2019/7

N2 - Many complex systems in biology, physics, and engineering include a large number of state variables (SVs), and measuring the full state of the system is often impossible. Typically, a set of sensors is used to measure a part of the SVs. A system is called observable if these measurements allow to reconstruct the entire state of the system. When the system is not observable, an important and practical problem is how to add a minimal number of sensors so that the system becomes observable. This minimal observability problem is practically useful and theoretically interesting, as it pinpoints the most informative nodes in the system. We consider the minimal observability problem for an important special class of Boolean networks (BNs), called conjunctive BNs (CBNs). Using a graph-Theoretic approach, we provide a necessary and sufficient condition for observability of a CBN with n SVs and an efficient algorithm for solving the minimal observability problem. The algorithm time complexity is linear in the length of the description of the CBN and in particular it is O(n 2). We demonstrate the usefulness of these results by studying the properties of a class of randomly generated CBNs.

AB - Many complex systems in biology, physics, and engineering include a large number of state variables (SVs), and measuring the full state of the system is often impossible. Typically, a set of sensors is used to measure a part of the SVs. A system is called observable if these measurements allow to reconstruct the entire state of the system. When the system is not observable, an important and practical problem is how to add a minimal number of sensors so that the system becomes observable. This minimal observability problem is practically useful and theoretically interesting, as it pinpoints the most informative nodes in the system. We consider the minimal observability problem for an important special class of Boolean networks (BNs), called conjunctive BNs (CBNs). Using a graph-Theoretic approach, we provide a necessary and sufficient condition for observability of a CBN with n SVs and an efficient algorithm for solving the minimal observability problem. The algorithm time complexity is linear in the length of the description of the CBN and in particular it is O(n 2). We demonstrate the usefulness of these results by studying the properties of a class of randomly generated CBNs.

KW - Boolean networks (BNs)

KW - computational complexity

KW - logical systems

KW - observability

KW - random graphs

KW - social networks

KW - systems biology

UR - http://www.scopus.com/inward/record.url?scp=85056742477&partnerID=8YFLogxK

U2 - 10.1109/TAC.2018.2882154

DO - 10.1109/TAC.2018.2882154

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AN - SCOPUS:85056742477

VL - 64

SP - 2727

EP - 2736

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 7

M1 - 8540082

ER -