Observability of Boolean networks: A graph-theoretic approach

Dmitriy Laschov, Michael Margaliot, Guy Even

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)2351-2362
Number of pages12
Issue number8
StatePublished - Aug 2013


  • Boolean control networks
  • Computational complexity
  • Gene regulating networks
  • Logical systems
  • Observability
  • Observable graphs
  • Systems biology

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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