Real-time recognition of languages on an two-dimensional Archimedean thread

• Venue: Theoretical Computer Science - Discrete applied problems, florilegium for E. Goles
• Year: 2004

Fine studies on how powerful are two-dimensional computing devices are restricted by the difficulty to set up a relevant notion of language of figures. In the case of two-dimensional cellular automata, several solutions have been proposed, but we adopt here another point of view: to the automaton is added a one-to-one "locally connected" mapping, τ, from Z (orN) onto Z2, we have named a thread. That leads to a notion of language (usual language of words) recognition depending on a thread, what in turn leads to complexity classes, especially classes of languages recognized in real time on such devices. Here we consider two-dimensional cellular automata with the discrete Archimedean spiral as thread, and we compare the class of languages recognized in real time by two-dimensional cellular automata with the Archimedean spiral to the class of languages recognized in real time by one-dimensional classical cellular automata.