Several types of systems of parallel communicating restarting automata are introduced andstudied. The main result shows that, for all types of restarting automata X, centralizedsystems of restarting automata of type X have the same computational power asnon-centralized systems of restarting automata of the same type and the same number ofcomponents. This result is proved by a direct simulation. In addition, it is shown thatfor one-way restarting automata without auxiliary symbols, systems of degree at least twoare more powerful than the component automata themselves. Finally, a lower and an upperbound are given for the expressive power of systems of parallel communicating restartingautomata.

In the literature various types of restarting automata have been studied that are basedon contextual rewriting. A word w is accepted by such an automaton if,starting from the initial configuration that corresponds to input w, theword w is reduced to the empty word by a finite number of applications ofthese contextual rewritings. This approach is reminiscent of the notion of McNaughtonfamilies of languages. Here we put the aforementioned types of restarting automata intothe context of McNaughton families of languages, relating the classes of languagesaccepted by these automata in particular to the class GCSL of growing context-sensitivelanguages and to the class CRL of Church–Rosser languages.

We study cooperating distributed systems (CD-systems) of stateless deterministic restarting automata with window size 1 that are equipped with an external pushdown store. In this way we obtain an automata-theoretical characterization for the class of word languages that are linearizations of context-free trace languages.

As already 2-monotone R-automata accept NP-complete languages, we introduce a restricted variant of j-monotonicity for restarting automata, called sequential j-monotonicity. For restarting automata without auxiliary symbols, this restricted variant still yields infinite hierarchies. However, for restarting automata with auxiliary symbols, all degrees of sequential monotonicity collapse to the first level, implying that RLWW-automata that are sequentially monotone of degree j for any j ≥ 1 only accept context-free languages.