The infinite dihedral group
We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.
math.GR↗
arXiv subjects
Jānis Buls
Publications and source records attributed to Jānis Buls.
The Lamplighter Group
We are following [4]. Nevertheless we are interested only in claryfication that the lamplighter group can be realized as a 2--states Mealy machine.
math.GR↗
Machine $B_4$
We construct map $ξ$. It exhibits dense orbits for all $x\in\overline{0,1}^ω$. We give elementary proofs for all statements.
math.GR↗
Automaton (Semi)groups (Basic Concepts)
In this paper, we give an introduction to basic concepts of automaton semigroups. While we must note that this paper does not contain new results, it is focused on extended introduction in the subject and detailed examples.
math.GR↗
The adaptation of Shamir's protocol for increasing the security of a mobile environment
The aim of the paper is to provide a solution which increases the security of a mobile environment for both individuals and for workers in an enterprise. The proposed solution adapts Shamir's approach for sharing a secret for encryption key management. One part of the key is stored on a Bluetooth (or NFC) wristband or on an enterprise server, while a mobile device is used to store all the rest. The approach can be applied for both securing documents and voice data. The solution is supported by a mathematical formality which is missing in the currently known advice within cryptographic folklore.
cs.CR↗