Bounded Languages Meet Cellular Automata with Sparse Communication
Abstract
Cellular automata are onedimensional arrays of interconnected interacting finite automata. We investigate one of the weakest classes, the realtime oneway cellular automata, and impose an additional restriction on their intercell communication by bounding the number of allowed uses of the links between cells. Moreover, we consider the devices as acceptors for bounded languages in order to explore the borderline at which nontrivial decidability problems of cellular automata classes become decidable. It is shown that even devices with drastically reduced communication, that is, each two neighboring cells may communicate only constantly often, accept bounded languages that are not semilinear. If the number of communications is at least logarithmic in the length of the input, several problems are undecidable. The same result is obtained for classes where the total number of communications during a computation is linearly bounded.
 Publication:

arXiv eprints
 Pub Date:
 July 2009
 arXiv:
 arXiv:0907.5128
 Bibcode:
 2009arXiv0907.5128K
 Keywords:

 Computer Science  Formal Languages and Automata Theory;
 Computer Science  Distributed;
 Parallel;
 and Cluster Computing
 EPrint:
 EPTCS 3, 2009, pp. 163172