Neural and automata networks: dynamical behavior and applications
Neural and automata networks: dynamical behavior and applications
One-way cellular automata on Cayley graphs
Theoretical Computer Science
Simulating quadratic dynamical systems is PSPACE-complete (preliminary version)
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
On the computational complexity of finite cellular automata
Journal of Computer and System Sciences
Models of massive parallelism: analysis of cellular automata and neural networks
Models of massive parallelism: analysis of cellular automata and neural networks
On the hardness of approximate reasoning
Artificial Intelligence
Finite automata-models for the investigation of dynamical systems
Information Processing Letters
Elements of a theory of computer simulation I: sequential CA over random graphs
Applied Mathematics and Computation
Elements of a theory of simulation II: sequential dynamical systems
Applied Mathematics and Computation
Discrete, sequential dynamical systems
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Complexity of Counting in Sparse, Regular, and Planar Graphs
SIAM Journal on Computing
Approximation Schemes Using L-Reductions
Proceedings of the 14th Conference on Foundations of Software Technology and Theoretical Computer Science
Reachability problems for sequential dynamical systems with threshold functions
Theoretical Computer Science - Mathematical foundations of computer science
Predecessor existence problems for finite discrete dynamical systems
Theoretical Computer Science
Computational aspects of analyzing social network dynamics
IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part III
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We study computational complexity of counting the fixed point configurations (FPs) in certain classes of graph automata viewed as discrete dynamical systems. We prove that both exact and approximate counting of FPs in Sequential and Synchronous Dynamical Systems (SDSs and SyDSs, respectively) are computationally intractable, even when each node is required to update according to a symmetric Boolean function. We also show that the problems of counting exactly the garden of Eden configurations (GEs), as well as all transient configurations, are in general intractable, as well. Moreover, exactly enumerating FPs or GEs remains hard even in some severely restricted cases, such as when the nodes of an SDS or SyDS use only two different symmetric Boolean update rules, and every node has a neighborhood size bounded by a small constant.