A novel algebraic and dynamic systems approach to finite elementary cellular automata is presented. In particular, simple algebraic expressions for the local rules of elementary cellular automata are deduced and the cellular automata configurations are represented via Fourier analysis. This allows for a further analysis of the global dynamics of cellular automata by the use of tools derived fro...

Automata and language theory study finitely presented mechanisms for generating languages. A language is a family of words. A slight shift in focus is very revealing. Instead of grammars and automata as language generators, one views them as propagators of possibly infinite labelled transition graphs. This is our starting point for pushdown automata. The main goal is to report on a proof of dec...

We give a new and simple proof of a key lemma on the rank of a matrix in Leung's paper [3], where he showed there exists a family of nondeterministic nite automata fAng, with n states and exponential ambiguity, such that any smallest equivalent polynomially ambiguous nite automaton has 2 1 states. Keyword: nondeterministic automata, ambiguity, automata theory.

This paper introduces several cellular automata in hyperbolic spaces which are able to simulate any computational device, as they are universal. We sketchily present five universal cellular automata, four of them on two grids of the hyperbolic plane and one in a grid of the hyperbolic 3D space. Key–Words: Theory of Computation, Cellular Automata, universality, hyperbolic geometry.

The purpose of this paper is to describe structural properties of automata whose transition semigroups have a zero, left zero, right zero or bi-zero, or are nilpotent extensions of rectangular bands, left zero bands or right zero bands, or are nilpotent. To describe the structure of these automata we use various well-known decomposition methods of automata theory – direct sum decompositions, su...

Abstract Sequence theories are an extension of strings with infinite alphabet letters, together a corresponding theory (e.g. linear integer arithmetic). Sequences natural abstractions extendable arrays, which permit wealth operations including append, map, split, and concatenation. In spite the growing amount tool support for sequences by leading SMT-solvers, little is known about decidability ...

Using a result of B.H. Neumann we extend Eilenberg’s Equality Theorem to a general result which implies that the multiplicity equivalence problem of two (nondeterministic) multitape finite automata is decidable. As a corollary we solve a long standing open problem in automata theory, namely, the equivalence problem for multitape deterministic finite automata. The main theorem states that there ...

In this paper a way to have structures with partiality in its internal structure in a categorical approach is presented and, with this, a category of partial graphs Grp is given and partial automata are constructed from Grp. With a simple categorical operation, computations of partial automata are given and can be seen as a part of the structure of partial automata. Keyworks: computation, parti...

This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results on embeddings of shifts of finite type. The second one is the connection between syntactic semigroups and the classification of sofic shifts up to conjugacy.