Type of Publication:  Contribution to a conference 
Author:  Kosub, Sven; Homan, Christopher M. 
Year of publication:  2007 
Conference:  ICTCS, Oct 3, 2007  Oct 5, 2007, Rome, Italy 
Published in:  Proceedings of the 10th Italian Conference on Theoretical Computer Science / Italiano, Giuseppe F. et al. (ed.).  Singapore [u.a.] : World Scientific, 2007.  pp. 163174 
Summary: 
We present dichotomy theorems regarding the computational complexity of counting fixed points in boolean (discrete) dynamical systems, i.e., finite discrete dynamical systems over the domain {0,1}. For a class F of boolean functions and a class G of graphs, an (F,G)system is a boolean dynamical system with local transitions functions lying in F and graphs in G. We show that, if local transition functions are given by lookup tables, then the following complexity classification holds: Let F be a class of boolean functions closed under superposition and let G be a graph class closed under taking minors. If F contains all minfunctions, all maxfunctions, or all selfdual and monotone functions, and G contains all planar graphs, then it is #Pcomplete to compute the number of fixed points in an (F,G)system; otherwise it is computable in polynomial time. We also prove a dichotomy theorem for the case that local transition functions are given by formulas (over logical bases). This theorem has a significantly more complicated structure than the theorem for lookup tables. A corresponding theorem for boolean circuits coincides with the theorem for formulas.

Subject (DDC):  004 Computer Science 
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KOSUB, Sven, Christopher M. HOMAN, 2007. Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems. ICTCS. Rome, Italy, Oct 3, 2007  Oct 5, 2007. In: ITALIANO, Giuseppe F., ed. and others. Proceedings of the 10th Italian Conference on Theoretical Computer Science. Singapore [u.a.]:World Scientific, pp. 163174
@inproceedings{Kosub2007Dicho3057, title={Dichotomy Results for Fixed Point Counting in Boolean Dynamical Systems}, year={2007}, address={Singapore [u.a.]}, publisher={World Scientific}, booktitle={Proceedings of the 10th Italian Conference on Theoretical Computer Science}, pages={163174}, editor={Italiano, Giuseppe F.}, author={Kosub, Sven and Homan, Christopher M.} }
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