Abstract

Devices of interconnected parallel acting sequential automata are investigated from a language theoretic point of view. Starting with the well-known result that each tally language acceptable by a classical one-way cellular automaton (OCA) in real-time has to be a regular language we will answer the three natural questions `How much time do we have to provide?' `How much power do we have to plug in the single cells (i.e., how complex has a single cell to be)?' and `How can we modify the mode of operation (i.e., how much nondeterminism do we have to add)?' in order to accept non-regular tally languages. We show the surprising result that for some classes of generalized interacting automata parallelism does not lead to more accepting power than obtained by a single sequential cell. Adding a wee bit of nondeterminism an infinite hierarchy of unary language families can be shown by allowing more and more nondeterminism.

Citations