We devise an algorithm which, given a bounded automaton A, decides whether the group generated by A is finite. The solution comes from description of infinite sequences having A-orbit using deterministic finite-state acceptor. This acceptor can also be used to decide acts level-transitively.

Abstract We show that the finite sequentiality problem is decidable for finitely ambiguous max-plus tree automata. A automaton a weighted over semiring. called if number of accepting runs on every bounded by global constant. The asks whether given automaton, there exist many deterministic automata whose pointwise maximum equivalent to automaton.

we prove that if $m$ is a monoid and $a$ a finite set with more than one element‎, ‎then the residual finiteness of $m$ is equivalent to that of the monoid consisting of all cellular automata over $m$ with alphabet $a$‎.

The existing algorithm to compute and verify the automata associated with an automatic group deals only with the subclass of shortlex automatic groups. This paper describes the extension of the algorithm to deal with automatic groups associated with other word orders (the algorithm has now been implemented) and reports on the use of the algorithm for specific examples; in particular a very natu...

We study definability and complexity issues for automatic and ω-automatic structures. These are, in general, infinite structures but they can be finitely presented by a collection of automata. Moreover, they admit effective (in fact automatic) evaluation of all first-order queries. Therefore, automatic structures provide an interesting framework for extending many algorithmic and logical method...

The Moore-Myhill Garden of Eden theorem asserts that a cellular automaton with finite alphabet over a free abelian group of rank 2 is surjective if and only if it is pre-injective. Here, pre-injectivity means that two configurations which coincide outside of a finite subset of the group must coincide everywhere if they have the same image under the cellular automaton. The Garden of Eden theorem...