One-Dimensional Cellular Automaton Transducers

The parallel models of cellular automata and iterative arrays are investigated towards their ability to compute transductions, that is, to transform inputs into outputs. The families of transductions computed are classified with regard to the time allowed to process the input and the output, respectively. The time complexities of real-time and linear-time are of particular interest. First, the computational capabilities of iterative array transducers are investigated and proper inclusions between real-time and linear-time can be obtained. Then, iterative array transducers and cellular automaton transducers are considered, that is, sequential input/output mode is compared to parallel input/output mode. Here, the result is that the parallel mode is not weaker than the sequential one, but with regard to certain time complexities the parallel mode is even more powerful than the sequential one. In the second part of the paper, cellular automaton transducers and iterative array transducers are compared with the conventional sequential transducer models, namely, finite state transducers and pushdown transducers. It turns out that unambiguous finite state transducers and deterministic pushdown transducers can be simulated by both parallel models, but cellular automaton transducers achieve a faster simulation than iterative array transducers.