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Francesca Fiorenzi

Publications and source records attributed to Francesca Fiorenzi.

6 recordsLinked to original sources
arXiv2014

Multipass automata and group word problems

We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean closure of the class of deterministic context-free languages while the class of languages accepted by nondeterministic multipass automata is exactly the class of poly-context-free languages, that is, languages which are the intersection of finitely many context-free languages. We illustrate the use of these automata by studying groups whose word problems are in the above classes.

math.GR↗
arXiv2014

Periodic configurations of subshifts on groups

We study the density of periodic configurations for shift spaces defined on (the Cayley graph of) a finitely generated group. We prove that in the case of a full shift on a residually finite group and in that of a group shift space on an abelian group, the periodic configurations are dense. In the one-dimensional case we prove the density for irreducible sofic shifts. In connection with this we study the surjunctivity of cellular automata and local selfmappings. Some related decision problems for shift spaces of finite type are also investigated.

cs.FL↗
arXiv2014

Cellular automata between sofic tree shifts

We study the sofic tree shifts of $A^{Σ^*}$, where $Σ^*$ is a regular rooted tree of finite rank. In particular, we give their characterization in terms of unrestricted Rabin automata. We show that if $X \subset A^{Σ^*}$ is a sofic tree shift, then the configurations in $X$ whose orbit under the shift action is finite are dense in $X$, and, as a consequence of this, we deduce that every injective cellular automata $τ\colon X \to X$ is surjective. Moreover, a characterization of sofic tree shifts in terms of general Rabin automata is given. We present an algorithm for establishing whether two unrestricted Rabin automata accept the same sofic tree shift or not. This allows us to prove the decidability of the surjectivity problem for cellular automata between sofic tree shifts. We also prove the decidability of the injectivity problem for cellular automata defined on a tree shift of finite type.

cs.FL↗
arXiv2012

Topological properties of cellular automata on trees

We prove that there do not exist positively expansive cellular automata defined on the full k-ary tree shift (for k>=2). Moreover, we investigate some topological properties of these automata and their relationships, namely permutivity, surjectivity, preinjectivity, right-closingness and openness.

cs.FL↗
arXiv2012

Cellular automata on regular rooted trees

We study cellular automata on regular rooted trees. This includes the characterization of sofic tree shifts in terms of unrestricted Rabin automata and the decidability of the surjectivity problem for cellular automata between sofic tree shifts.

cs.FL↗