Abstract
This paper studies problems of completing a given Boolean network (Boolean circuit) so that the input/output behavior is consistent with given examples, where we only consider acyclic networks. These problems arise in the study of inference of signaling networks using reporter proteins. We prove that these problems are NP-complete in general and a basic version remains NP-complete even for tree structured networks. On the other hand, we show that these problems can be solved in polynomial time for partial k-trees of bounded (constant) indegree if a logarithmic number of examples are given.
This work is partially supported by the Cell Array Project from NEDO, Japan and by a Grant-in-Aid ‘Systems Genomics’ from MEXT, Japan.
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References
Akutsu, T., Miyano, S., Kuhara, S.: Identification of genetic networks from a small number of gene expression patterns under the Boolean network model. In: Proc. Pacific Symposium on Biocomputing 1999, pp. 17–28 (1999)
Akutsu, T., Kuhara, S., Maruyama, O., Miyano, S.: Identification of genetic networks by strategic gene disruptions and gene overexpressions under a Boolean model. Theoretical Computer Science 298, 235–251 (2003)
Akutsu, T., Hayashida, M., Ching, W.-K., Ng, M.K.: Control of Boolean networks: Hardness results and algorithms for tree structured networks. Journal of Theoretical Biology 244, 670–679 (2007)
Angluin, D., Aspnes, J., Chen, J., Wu, Y.: Learning a circuit by injecting values. In: Proc. 38th Annual ACM Symposium on Theory of Computing, pp. 584–593 (2006)
Angluin, D., Aspnes, J., Chen, J., Reyzin, L.: Learning large-alphabet and analog circuits with value injection queries. Machine Learning 72, 113–138 (2008)
Angluin, D., Aspnes, J., Chen, J., Eisenstat, D., Reyzin, L.: Learning acyclic probabilistic circuits using test paths. In: Proc. 21st Annual Conference on Learning Theory, pp. 169–180 (2008)
Bodlaender, H.L.: A linear-time algorithm for finding tree-decompositions of small treewidth. SIAM Journal on Computing 25, 1305–1317 (1996)
Flum, J., Grohe, M.: Parameterized Complexity Theory. Springer, Berlin (2006)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Co., New York (1979)
Gupta, S., Bisht, S.S., Kukreti, R., Jain, S., Brahmachari, S.K.: Boolean network analysis of a neurotransmitter signaling pathway. Journal of Theoretical Biology 244, 463–469 (2007)
Ideker, T.E., Thorsson, V., Karp, R.M.: Discovery of regulatory interactions through perturbation: inference and experimental design. In: Proc. Pacific Symposium on Biocomputing 2000, pp. 302–313 (2000)
Kauffman, S.A.: The Origins of Order: Self-organization and Selection in Evolution. Oxford Univ. Press, NY (1993)
Kearns, M.J., Vazirani, U.V.: An Introduction to Computational Learning Theory. MIT Press, Cambridge (1994)
Mochizuki, A.: Structure of regulatory networks and diversity of gene expression patterns. Journal of Theoretical Biology 250, 307–321 (2008)
Pitt, L., Valiant, L.G.: Computational limitations on learning from examples. Journal of the ACM 35, 965–984 (1988)
Tokumoto, Y., Horimoto, K., Miyake, J.: TRAIL inhibited the cyclic AMP responsible element mediated gene expression. Biochemical and Biophysical Research Communications 381, 533–536 (2009)
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Akutsu, T., Tamura, T., Horimoto, K. (2009). Completing Networks Using Observed Data. In: Gavaldà, R., Lugosi, G., Zeugmann, T., Zilles, S. (eds) Algorithmic Learning Theory. ALT 2009. Lecture Notes in Computer Science(), vol 5809. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04414-4_14
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DOI: https://doi.org/10.1007/978-3-642-04414-4_14
Publisher Name: Springer, Berlin, Heidelberg
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