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.

∗to whom correspondence should be addressed †The complete list of members of the Consortium for Logical Models and Tools is provided in the Acknowledgement section. CoLoMoTo-position-paper-bioRxiv-preprint 1/15. CC-BY-ND 4.0 International licensenot peer-reviewed) is the author/funder. It is made available under a The copyright holder for this preprint (which was. http://dx.doi.org/10.1101/010504doi: bioRxiv preprint first posted online Oct. 19, 2014; The identification of large regulatory and signalling networks involved in the control of crucial cellular processes calls for proper modelling approaches. Indeed, models can help elucidate properties of these networks, understand their behaviour, and provide (testable) predictions by performing in silico experiments. In this context, qualitative, logical frameworks have emerged as relevant approaches as demonstrated by a growing number of published models, along with new method-ologies and software tools. This productive activity now requires a concerted effort to ensure model reusability and interoperability between tools. Here, we outline the logical modelling framework and present the most important achievements of

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Abstract — The precise inner workings of cellular mechanisms remain largely unknown and, therefore, their modeling is usually based on conjectures. The availability of large amounts of genetic data, and the lack of abstract mathematical models, makes computer algorithms the only tool available for searching for these hypothetical realities. We call the conjectured algorithmic-independent reality that underlies the method design and intention, the semantics of the algorithm. This article is a brief semantics analysis exercise performed with four binary quantization algorithms for time series of gene expression data. Keywords- binary quantization; gene expression; quantitative semantics I.