Communication complexity and intrinsic universality in cellular automata
نویسندگان
چکیده
منابع مشابه
Communication complexity and intrinsic universality in cellular automata
Let F be a cellular automaton (CA). This paper establishes necessary conditions for F in order to be intrinsically universal. The central idea is to consider the communication complexity of various “canonical problems” related to the dynamics of F . We show that the intrinsic universality of F implies high communication complexity for each of the canonical problems. This result allows us to rul...
متن کاملUniversality and Complexity in Cellular Automata
Cellular automata are discrete dynamical systems with simple construction but complex self-organizing behaviour. Evidence is presented that all one-dimensional cellular automata fall into four distinct universality classes. Characterizations of the structures generated in these classes are discussed. Three classes exhibit behaviour analogous to limit points, limit cycles and chaotic attractors....
متن کاملCellular automata and communication complexity
The model of cellular automata is fascinating because very simple local rules can generate complex global behaviors. The relationship between local and global function is subject of many studies. We tackle this question by using results on communication complexity theory and, as a by-product, we provide (yet another) classification of cellular automata.
متن کاملErratum to: "Communication Complexity and Intrinsic Universality in Cellular Automata" [Theor. Comput. Sci 412 (1-2) (2011) 2-21]
Proofs of Propositions 6 and 8 of the paper Communication Complexity and Intrinsic Universality in Cellular Automata are formally incorrect. This erratum proves weaker versions of Propositions 6 and 8 and a stronger version of Proposition 9which are sufficient to get the main results of the paper (Corollary 2) for PREDICTION and INVASION problems. For problem CYCLE, we only prove a weaker versi...
متن کاملUniversality and Cellular Automata
The classification of discrete dynamical systems that are computationally complete has recently drawn attention in light of Wolfram’s “Principle of Computational Equivalence”. We discuss a classification for cellular automata that is based on computably enumerable degrees. In this setting the full structure of the semilattice of the c.e. degrees is inherited by the cellular automata. 1 Intermed...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2011
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2010.10.005