2 citations · 3 across the 7 of their papers we have counts for
8 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…
One-variable equations over the lamplighter group
Alexander Ushakov, Yankun Wang
We study one-variable equations over the lamplighter group $L_2=\MZ_2 \wr \MZ$. While the decidability of arbitrary equations over remains open, we prove that the Diophantine…
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…
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…
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…
Constrained inhomogeneous spherical equations: average-case hardness
Alexander Ushakov
In this paper we analyze computational properties of the Diophantine problem (and its search variant) for spherical equations (and its variants…