On CD-systems of stateless deterministic R-automata with window size one

Here we study cooperating distributed systems (CD-systems) of restarting automata that are very restricted: they are deterministic, they cannot rewrite, but only delete symbols, they restart immediately after performing a delete operation, they are stateless, and they have a read/write window of size 1 only, that is, these are stateless deterministic R(1)R(1)-automata. We study the expressive power of these systems by relating the class of languages that they accept by mode =1 computations to other well-studied language classes, showing in particular that this class only contains semi-linear languages. Our model can be viewed as a nondeterministic finite-state acceptor with translucent letters, that is, it processes its input in a different way than the usual left-to-right order. In this way all commutative semi-linear languages, and in fact all rational trace languages, can be accepted. In addition, we investigate the closure and non-closure properties of the class of languages accepted by our model and some of its algorithmic properties.

► Stateless deterministic restarting automata are studied.
► An infinite hierarchy of language classes is obtained based on the window size.
► CD-systems of these automata with window size one are introduced.
► A characterization of the rational trace languages by these CD-systems is presented.
► Closure and non-closure properties of the corresponding language class are derived.