Communication complexity
Inducing an order on cellular automata by a grouping operation
Discrete Applied Mathematics
Communication Complexity and Sequential Compuation
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Some complexity questions related to distributive computing(Preliminary Report)
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
Cellular automata and communication complexity
Theoretical Computer Science - Discrete applied problems, florilegium for E. Goles
Computation: finite and infinite machines
Computation: finite and infinite machines
Theory of Self-Reproducing Automata
Theory of Self-Reproducing Automata
Theoretical Computer Science
ISAAC '08 Proceedings of the 19th International Symposium on Algorithms and Computation
P-completeness of cellular automaton rule 110
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Communication complexity in number-conserving and monotone cellular automata
Theoretical Computer Science
Traced communication complexity of cellular automata
Theoretical Computer Science
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
Letting Alice and Bob choose which problem to solve: Implications to the study of cellular automata
Theoretical Computer Science
The two-handed tile assembly model is not intrinsically universal
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 5.23 |
The notions of universality and completeness are central in the theories of computation and computational complexity. However, proving lower bounds and necessary conditions remains hard in most cases. In this article, we introduce necessary conditions for a cellular automaton to be ''universal'', according to a precise notion of simulation, related both to the dynamics of cellular automata and to their computational power. This notion of simulation relies on simple operations of space-time rescaling and it is intrinsic to the model of cellular automata. Intrinsic universality, the derived notion, is stronger than Turing universality, but more uniform, and easier to define and study. Our approach builds upon the notion of communication complexity, which was primarily designed to study parallel programs, and thus is, as we show in this article, particulary well suited to the study of cellular automata: it allowed us to show, by studying natural problems on the dynamics of cellular automata, that several classes of cellular automata, as well as many natural (elementary) examples, were not intrinsically universal.