We state and study the congruence subgroup problem for groups acting on rooted tree, and for branch groups in particular. The problem is reduced to the computation of the congruence kernel, which we split into two parts: the branch kernel and the rigid kernel. In the case of regular branch groups, we prove that the first one is Abelian while the second has finite exponent. We also establish som...

The notion of transducer integer sequences is considered through a series of examples (the chosen examples are related to the Tower of Hanoi problem on 3 pegs). By definition, transducer integer sequences are integer sequences produced, under a suitable interpretation, by finite transducers encoding rational tree morphisms (length and prefix preserving transformations of words that have only fi...

The ability to acquire a cognitive and motor skill was investigated in 20 older and 20 younger participants using repeated testing on the Tower of Toronto (TT) puzzle, a variant of the Tower of Hanoi. Explicit memory, perceptual priming, and sustained attention were also assessed. Older subjects exhibited a defective cognitive skill performance despite the fact that cognitive skill learning suf...

For the Tower of Hanoi problem, it has been found that it is possible to construct a nice graph with legal states of the Tower of Hanoi as the vertices and legal moves between legal states as the edges between corresponding vertices. This “Hanoi graph” we denote by Hk n for k pegs and n disks. Our motivation is to describe the properties of this graph for k ≥ 4 and to describe a class of graphs...

OBJECTIVE To assess the effect of ischemic infarctions affecting the basal ganglia (BG) region on a series of procedural learning tasks. BACKGROUND The basal ganglia hypothesis of procedural learning is a matter of debate. As most of the relevant research so far is based on examination of patients suffering from Parkinson disease, this inconsistency might reflect either lesion heterogeneity e...