On real-time cellular automata and trellis automata
Acta Informatica
Some relations between massively parallel arrays
Parallel Computing - Special issue: cellular automata
Signals in one-dimensional cellular automata
Theoretical Computer Science - Special issue: cellular automata
Reversal-Bounded Multicounter Machines and Their Decision Problems
Journal of the ACM (JACM)
Parallel Computing - Special issue on cellular automata: from modeling to applications
Fundamenta Informaticae - Special issue on cellular automata
Linear Time Language Recognition on Cellular Automata with Restricted Communication
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Descriptional complexity of cellular automata and decidability questions
Journal of Automata, Languages and Combinatorics - Third international workshop on descriptional complexity of automata, grammars and related structures
Real-time generation of primes by a 1-bit-communication cellular automaton
Fundamenta Informaticae - Special issue on cellular automata
Fast reversible language recognition using cellular automata
Information and Computation
Cellular automata and formal languages
SWAT '70 Proceedings of the 11th Annual Symposium on Switching and Automata Theory (swat 1970)
Fast iterative arrays with restricted inter-cell communication: constructions and decidability
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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We investigate cellular automata whose internal inter-cell communication is bounded. The communication is quantitatively measured by the number of uses of the links between cells. Bounds on the sum of all communications of a computation as well as bounds on the maximal number of communications that may appear between each two cells are considered. It is shown that even the weakest non-trivial device in question, that is, one-way cellular automata where each two neighboring cells may communicate constantly often only, accept rather complicated languages. We investigate the computational capacity of the devices in question and prove an infinite strict hierarchy depending on the bound on the total number of communications during a computation. Despite their sparse communication even for the weakest devices, by reduction of Hilbert's tenth problem the undecidability of several problems is derived. Finally, the question of whether a given real-time one-way cellular automaton belongs to the weakest class is shown to be undecidable. This result can be used to answer an open question.