Walking automata, be they running over words, trees or even graphs, possibly extended with pebbles that can be dropped and lifted on vertices, have long been defined and studied in Computer Science. However, questions concerning walking automata are surprisingly complex to solve. In this paper, we study a generic notion of walking automata over graphs whose semantics naturally lays within inver...

A sequential automatic algebra is a structure of the type (A; f1, . . . , fn), where A is recognised by a finite automaton, and functions f1, . . . , fn are total operations on A that are computed by inputoutput automata. Our input-output automata are variations of Mealy automata. We study some of the fundamental properties of these algebras and provide many examples. We give classification res...

The algebraic hierarchical decomposition of finite state automata can be applied wherever a finite system should be ‘understood’ using a hierarchical coordinate system. Here we use the holonomy decomposition for characterizing finite automata using derived hierarchical structure. This leads to a characterization according to the existence of different cycles within an automaton. The investigati...

This paper addresses the torsion problem for a class of automaton semigroups, defined as semigroups of transformations induced by Mealy automata, aka letter-by-letter transducers with the same input and output alphabet. The torsion problem is undecidable for automaton semigroups in general, but is known to be solvable within the well-studied class of (semi)groups generated by invertible bounded...

In [Gut89] Howard Gutowitz writes : “A fundamental problem in theory of cellular automata is classification. A good classification divides cellular automata into groups with meaningfully related properties. In general there are two types of classifications : phenotypic and genotypic. A phenotypic classification divides a population into groups according to their observed behaviour. A genotypic ...

We prove that the word problem is undecidable in functionally recursive groups, and that the order problem is undecidable in automata groups, even under the assumption that they are contracting.

This paper gives a tableau-based technique for converting formulas in finite propositional linear-time temporal logic (Finite LTL) into finite-state automata whose languages are the models of given formula. Finite LTL differs from traditional that interpreted with respect to finite, rather than infinite, sequences states; this fact means automata, ω -automata such as those developed by Büchi an...