Abstract
We consider the problem of inferring the local transition functions of discrete dynamical systems from observed behavior. Our focus is on synchronous systems whose local transition functions are threshold functions. We assume that the topology of the system is known and that the goal is to infer a threshold value for each node so that the system produces the observed behavior. We show that some of these inference problems are efficiently solvable while others are NP-complete, even when the underlying graph of the dynamical system is a simple path. We also identify a fixed parameter tractable problem in this context.
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Notes
- 1.
We will use the term “stable configuration” instead of “fixed point” throughout this paper since we will be using the word “fixed” in the context of fixed parameter tractability.
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Acknowledgments
We thank the reviewers for carefully reading the manuscript and providing valuable suggestions. This work has been partially supported by DTRA Grant HDTRA1-11-1-0016 and DTRA CNIMS Contract HDTRA1-11-D-0016-0010, NSF NetSE Grant CNS-1011769, NSF SDCI Grant OCI-1032677 and NIH MIDAS Grant 5U01GM070694-11.
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Adiga, A., Kuhlman, C.J., Marathe, M.V., Ravi, S.S., Rosenkrantz, D.J., Stearns, R.E. (2015). Complexity of Inferring Local Transition Functions of Discrete Dynamical Systems. In: Drewes, F. (eds) Implementation and Application of Automata. CIAA 2015. Lecture Notes in Computer Science(), vol 9223. Springer, Cham. https://doi.org/10.1007/978-3-319-22360-5_3
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DOI: https://doi.org/10.1007/978-3-319-22360-5_3
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