6 papers
Beyond Feedforward Networks: Reentry Neural Systems as the Fundamental Basis of Subjecthood and Intrinsic Safety of Next-Generation AGI
A. S. Ushakov, Yu. N. Berdinsk
We propose a complete architectural blueprint for safe artificial general intelligence based on a closed reentry loop (D <-> I cycle). In contrast to feedforward networks, which ar…
HNN extensions of free groups with equal associated subgroups of finite index: polynomial time word problem
Hanwen Shen, Alexander Ushakov
Let be an HNN extension of a free group with two equal associated normal subgroups of finite index. We prove that the word problem in is decidable…
One-variable equations over the lamplighter group
Alexander Ushakov, Yankun Wang
We study one-variable equations over the lamplighter group $\MZ_2 \wr \MZ$. While the decidability of arbitrary equations over remains open, we prove that the Diophantine pro…
One variable equations over the lamplighter group
Alexander Ushakov, Yankun Wang
We prove that one variable equations in the lamplighter group $\MZ_2\wr \MZ$ are decidable and describe an algorithm for solving such equations. The algorithm has super-exponential…
Orientable quadratic equations in wreath products
Alexander Ushakov, Chloe Weiers
In this paper we study the complexity of solving orientable quadratic equations in wreath products of finitely generated abelian groups. We give a classification of cases…
Quadratic equations in the lamplighter group
Alexander Ushakov, Chloe Weiers
In this paper we study the complexity of solving quadratic equations in the lamplighter group. We give a complete classification of cases (depending on genus and other characterist…