Automata arrays and context-free languages
Where mathematics, computer science, linguistics and biology meet
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
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
On two-way communication in cellular automata with a fixed number of cells
Theoretical Computer Science - Descriptional complexity of formal systems
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We investigate a restricted one-way cellular automaton (OCA) model where the number of cells is bounded by a constant number k, so-called kC-OCAs. In contrast to the general model, the generative capacity of the restricted model is reduced to the set of regular languages. A kC-OCA can be algorithmically converted to a deterministic finite automaton (DFA). The blow-up in the number of states is bounded by a polynomial of degree k. We can exhibit a family of unary languages which shows that this upper bound is tight in order of magnitude. We then study upper and lower bounds for the trade-off when converting DFAs to kC-OCAs. We show that there are regular languages where the use of kC-OCAs cannot reduce the number of states when compared to DFAs. We then investigate trade-offs between kC-OCAs with different numbers of cells and finally treat the problem of minimizing a given kC-OCA.