S. Wolfram, Undecidability and Intractability in Theoretical Physics, Phys. Rev. Lett. 54 (1985) 735. Home/Search Document Not in Database Summary APS Related Articles Check |
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Parallel Complex Systems Simulation - Schoneveld (1999) (1 citation) (Correct)
....of computational irreducibility. The problem of determining the configuration of a CA after t time steps, given an initial seed and the CA rule, can be solved in O(log t) time for the CAs in Figure 1. The evolution for the two other rules can only be found by explicit simulation with length O(t)[165]. The difference is that the former two are reducible and the latter two are irreducible, i.e. their ultimate behavior can only be predicted by explicit simulation. For infinite class IV CA it is effectively undecidable whether a particular rule operating on a particular initial seed will ....
....two are reducible and the latter two are irreducible, i.e. their ultimate behavior can only be predicted by explicit simulation. For infinite class IV CA it is effectively undecidable whether a particular rule operating on a particular initial seed will ultimately lead to a frozen state or not [89, 165]. Obviously this decision problem is not undecidable for finite CA, because it is always possible to determine its fate in at most k N steps, for k states and N cells. In Section 1.2.3 we will discuss the concepts of irreducibility and undecidability in more detail. Summarizing CA behavior: ....
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S. Wolfram. Undecidability and intractability in theoretical physics. Phys. Rev. Let., 54:735--738, 1985. In: Cellular Automata and Complexity.
Inaccessibility And Undecidability In Computation, Geometry.. - Saito, Kaneko (2001) (Correct)
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S. Wolfram, Undecidability and Intractability in Theoretical Physics, Phys. Rev. Lett. 54 (1985) 735.
Emergent Evolutionary Dynamics of Self-Reproducing Cellular.. - Salzberg (2003) (Correct)
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S. Wolfram. Undecidability and intractability in theoretical physics. Phys. Rev. Lett., 55:735-- 738, 1985.
The Topological Skeleton of Cellular Automaton Dynamics - Gutowitz, Domain (1996) (2 citations) (Correct)
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S. Wolfram, Undecidability and intractability in theoretical physics Phys. Rev. Lett. 54:735 (1985)
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