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Linear cellular automata and the garden-of-eden
TLDR
A solution to the All-Ones Problem can be described by a subset of all squares (namely a set of squares whose buttons when pressed in an arbitrary order will render all lights on) rather than a sequence. Expand
Computation theory of cellular automata
TLDR
The sets of configurations generated after a finite number of time steps of cellular automaton evolution are shown to form regular languages and it is suggested that such undecidability is common in these and other dynamical systems. Expand
On the Computational Complexity of Finite Cellular Automata
  • Klaus Sutner
  • Computer Science, Mathematics
  • J. Comput. Syst. Sci.
  • 1 February 1995
TLDR
The problem of deciding whether a configuration has a predecessor is shown to be NLOG-complete for one-dimensional cellular automata, and the question whether a target configuration occurs in the orbit of a source configuration may be P- complete, NP-complete or PSPACE-complete, depending on the type of cellular automaton. Expand
On σ-Automata
  • Klaus Sutner
  • Mathematics, Computer Science
  • Complex Syst.
  • 1 February 1988
The σ-game and cellular automata
1. SummaryIn an article in this journal Don Pelletier discussed the mathematics involved in a little battery operated toy called Merlin (see [3], and also the “Addenda” in this Monthly, Dec. 1987,Expand
De Bruijn Graphs and Linear Cellular Automata
TLDR
Every recursive configuration that has a predecessor on a linear CA already has a recursive pr edecessor, and it is shown that it is in genera l impossible to comput e such a predecessor effect ively. Expand
Classifying circular cellular automata
We introduce a hierarchy of linear cellular automata based on their limiting behavior on spatially periodic configurations. We show that it is undecidable to which class in the hierarchy a cellularExpand
Additive Automata On Graphs
  • Klaus Sutner
  • Mathematics, Computer Science
  • Complex Syst.
  • 1 December 1988
TLDR
The prob lem of deciding whether a given con­ figuration has a predecessor is solvable in polynomial t ime or NP-complete is investigated and a linear algorithm is given to decide reversibility of unicyclic graphs. Expand
- Automata and Chebyshev-PolynomialsKlaus
A-automaton is a simple additive, binary cellular automaton on a graph. For product graphs such as a grids and cylinders, reversibility and periodicity properties of the corresponding automaton canExpand
The Complexity of the Residual Node Connectedness Reliability Problem
TLDR
It is proven that the problem of computing the residual connectedness reliability is NP-hard by showing that the problems of counting the number of node induced connected subgraphs of a given graph is-complete. Expand
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