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- Ievgen Bondarenko, Rostislav Grigorchuk, Rostyslav Kravchenko, Yevgen Muntyan, Volodymyr Nekrashevych, Dmytro Savchuk +1 other
- 2008

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.

Zoraň Suni´c Cayley graph automatic groups are not necessarily Cayley grap

- ZORAN ŠUNIĆ
- 2006

Let a and b be positive, relatively prime integers. We show that the following are equivalent: (i) d is a dead end in the (symmetric) Cayley graph of Z with respect to a and b, (ii) d is a Frobenius value with respect to a and b (it cannot be written as a non-negative or non-positive integer linear combination of a and b), and d is maximal (in the Cayley… (More)

A connection relating Tamari lattices on symmetric groups regarded as lattices under the weak Bruhat order to the positive monoid P of Thompson group F is presented. Tamari congruence classes correspond to classes of equivalent elements in P. The two well known normal forms in P correspond to endpoints of intervals in the weak Bruhat order that determine… (More)

This note records some observations concerning geodesic growth functions. If a nilpotent group is not virtually cyclic then it has exponential geodesic growth with respect to all finite generating sets. On the other hand, if a finitely generated group G has an element whose normal closure is abelian and of finite index, then G has a finite generating set… (More)

- Zoran Šunić
- 2006

For each prime p and a monic polynomial f , invertible over p, we define a group G p,f of p-adic automorphisms of the p-ary rooted tree. The groups are modeled after the first Grigorchuk group, which in this setting is the group G 2,x 2 +x+1. We show that the constructed groups are self-similar, regular branch groups. This enables us to calculate the… (More)

We show that every right-angled Artin group AΓ defined by a graph Γ of finite chromatic number is poly-free with poly-free length bounded between the clique number and the chromatic number of Γ. Further, a characterization of all right-angled Artin groups of poly-free length 2 is given, namely the group AΓ has poly-free length 2 if and only if there exists… (More)

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 ⊂ 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… (More)

We introduce the notion of a normal gallery, a gallery in which any configuration of guards that visually covers the walls necessarily covers the entire gallery. We show that any star gallery is normal and any gallery with at most two reflex corners is normal. A polynomial time algorithm is provided deciding if, for a given gallery and a finite set of… (More)