Publikation: Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems
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A complete classification of the computational complexity of the fixed-point existence problem for Boolean dynamical systems, i.e., finite discrete dynamical systems over the domain {0, 1}, is presented. For function classes F and graph classes G, an (F, G)-system is a Boolean dynamical system such that all local transition functions lie in F and the underlying graph lies in G. Let F be a class of Boolean functions which is closed under composition and let G be a class of graphs which is closed under taking minors. The following dichotomy theorems are shown: (1) If F contains the self-dual functions and G contains the planar graphs, then the fixed-point existence problem for (F, G)-systems with local transition function given by truth-tables is NPcomplete; otherwise, it is decidable in polynomial time. (2) If F contains the self-dual functions and G contains the graphs having vertex covers of size one, then the fixed-point existence problem for (F, G)-systems with local transition function given by formulas or circuits is NP-complete; otherwise, it is decidable in polynomial time.
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KOSUB, Sven, 2008. Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems. In: Mathematics in Computer Science. 2008, 1(3), pp. 487-505. Available under: doi: 10.1007/s11786-007-0038-yBibTex
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title={Dichotomy Results for Fixed-Point Existence Problems for Boolean Dynamical Systems},
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volume={1},
journal={Mathematics in Computer Science},
pages={487--505},
author={Kosub, Sven}
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