Discrete dynamical systems on graphs and boolean functions

Authors:
Chris L. Barrett;William Y. C. Chen;Michelle J. Zheng
Affiliations:
Los Alamos National Laboratory, CCS-5, MS M997, Los Alamos, NM;Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China;Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China
Venue:
Mathematics and Computers in Simulation
Year:
2004

Citing 7
Cited 1

Regular Article: Acyclic Orientations of Random Graphs

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Elements of a theory of computer simulation I: sequential CA over random graphs

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Elements of a theory of simulation II: sequential dynamical systems

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Discrete, sequential dynamical systems

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Regular Article: On Acyclic Orientations and Sequential Dynamical Systems

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ETS IV: sequential dynamical systems: fixed points, invertibility and equivalence

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Decomposition and simulation of sequential dynamical systems

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Parallel discrete dynamical systems on independent local functions

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Abstract

Discrete dynamical systems based on dependency graphs have played an important role in the mathematical theory of computer simulations. In this paper, we are concerned with parallel dynamical systems (PDS) and sequential dynamical systems (SDS) with the OR and NOR functions as local functions. It has been recognized by Barrett, Mortveit and Reidys that SDS with the NOR function are closely related to combinatorial properties of the dependency graphs. We present an evaluation scheme for systems with the OR and NOR functions which can be used to clarify some basic properties of the dynamical systems. We show that for forests that does not contain a single edge the number of orientations equals the number of different OR-SDS.