Communicating sequential processes
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On totalistic systolic networks
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Undecidability of CA classification schemes
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On the limit sets of cellular automata
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Cellular automata: theory and experiment
Cellular automata: theory and experiment
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Asynchronous automata versus asynchronous cellular automata
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One-way cellular automata on Cayley graphs
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Inversion of 2D cellular automata: some complexity results
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Reachability analysis of dynamical systems having piecewise-constant derivatives
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On the computational complexity of finite cellular automata
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On the computational power of neural nets
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Models of massive parallelism: analysis of cellular automata and neural networks
Models of massive parallelism: analysis of cellular automata and neural networks
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Uniform approaches to the verification of finite state systems
Uniform approaches to the verification of finite state systems
Complexity of equivalence problems for concurrent systems of finite agents
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On Communicating Finite-State Machines
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Discrete, sequential dynamical systems
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On the complexity of verifying concurrent transition systems
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Switching and Finite Automata Theory: Computer Science Series
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Computational complexity of neural networks: a survey
Nordic Journal of Computing
On some Relations between Dynamical Systems and Transition Systems
ICALP '94 Proceedings of the 21st International Colloquium on Automata, Languages and Programming
On the Complexity of Relational Problems for Finite State Processes (Extended Abstract)
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Reachability problems for sequential dynamical systems with threshold functions
Theoretical Computer Science - Mathematical foundations of computer science
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Advances in Applied Mathematics
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CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
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ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part II
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On the Dynamics of Social Balance on General Networks (with an application to XOR-SAT)
Fundamenta Informaticae - Machines, Computations and Universality, Part II
Reversible iterative graph processes
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Proceedings of the Winter Simulation Conference
International Journal of Data Mining and Bioinformatics
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Sequential Dynamical Systems (SDSs) are a special type of finite discrete dynamical systems that can be used to model simulation systems. We focus on the computational complexity of testing several phase space properties of SDSs. Our main result is a sharp delineation between classes of SDSs whose behavior is easy to predict and those whose behavior is hard to predict. Specifically, we show the following. 1.Several state reachability problems for SDSs are PSPACE-complete, even when restricted to SDSs whose underlying graphs are of bounded bandwidth (and hence of bounded pathwidth and treewidth), and the function associated with each node is symmetric. Moreover, this result holds even when the underlying graph is d-regular for some constant d and all the nodes compute the same symmetric Boolean function. An immediate corollary of this result is a PSPACE-hard lower bound on the complexity of reachability problems for regular generalized 1D-Cellular Automata and undirected systolic networks with Boolean totalistic local transition functions. 2.In contrast, the above reachability problems are solvable in polynomial time for SDSs when the Boolean function associated with each node is symmetric and monotone. The PSPACE-completeness results follow as corollaries of simulation results which show for several classes of SDSs, how one class of SDSs can be efficiently simulated by another (more restricted) class of SDSs. We also prove several structural properties concerning the phase space of an SDS. SDSs are closely related to Cellular Automata (CA), concurrent transition systems, discrete Hopfield networks and systolic networks. This observation in conjunction with our lower bounds for SDSs, yields new PSPACE-hard lower bounds on the complexity of state reachability problems for these models, extending some of the earlier results in [K. Culik II, J. Karhumaki, On totalistic systolic networks, Inform. Process. Lett. 26 (5) (1988) 231-236; P. Floreen, E. Goles, G. Weisbuch, Transient length in sequential iterations of threshold functions, Discrete Appl. Math. 6 (1983) 95-98; P. Floreen, P. Orponen, Complexity issues in discrete Hopfield networks, Research Report No. A-1994-4, Department of Computer Science, University of Helsinki, 1994. Also appears in: I. Parberry (Ed.), Comp. and Learning Complexity of Neural Networks: Advanced Topics, 1999; D. Harel, O. Kupferman, M.Y. Vardi, On the complexity of verifying concurrent transition systems, Inform. and Comput. 173 (2002) 143-161; S.K. Shukla, H.B. Hunt III, D.J. Rosenkrantz, R.E. Stearns, On the complexity of relational problems for finite state processes, in: International Colloquium on Automata Programming and Languages, ICALP, 1996, pp. 466-477; A. Rabinovich, Complexity of equivalence problems for concurrent systems of finite agents, Inform. and Comput. 127 (2) (1997) 164-185].