There are many decision problems in automata theory (including membership, emptiness, emptiness of intersection, inclusion and universality problems) that for some classes of tree automata are NP-hard. The study of their parameterized complexity allows us to find new bounds of their non-polynomial time algorithmic behaviors. We present results of such a study for classical tree automata (TA), r...

In the paper we develop the p-adic theory of discrete automata. Every automaton A (transducer) whose input/output alphabets consist of p symbols can be associated to a continuous (in fact, 1-Lipschitz) map from padic integers to p integers, the automaton function fA. The p-adic theory (in particular, the p-adic ergodic theory) turned out to be very efficient in a study of properties of automata...

In order to explain the purpose of this paper, we recall briefly how the theory of “rationality” developed in the last fourty years. The theory of sets of finite strings recognized by finite automata, also known as regular or rational sets was developed in the fifties. It rapidly extended in two directions. Indeed, by solving the decidability problem of the second order monadic theory of one su...

This two-part article reviews selected problems in the theory of cellular automata, aiming to locate this theory with respect to the theory of complex systems in general. To appear in the journal "Complexity". 1 Figure 1: De schelp (conus marmoreus) This Rembrandt (1650) etching describes a shell bearing markings similar to those produced by some cellular automata.

A well-known theorem in automata theory states that every context-free language is accepted by a pushdown automaton. We investigate this theorem in the setting of processes, using the rooted branching bisimulation and contrasimulation equivalences instead of language equivalence. In process theory, different from automata theory, interaction is explicit, so we realize a pushdown automaton as a ...