6 citations · 9 across the 7 of their papers we have counts for
7 papers
CayleyPy-4: AI-Holography. Towards analogs of holographic string dualities for AI tasks
A. Chervov, F. Levkovich-Maslyuk, A. Smolensky +41
This is the fourth paper in the CayleyPy project, which applies AI methods to the exploration of large graphs. In this work, we suggest the existence of a new discrete version of h…
Biregular bipartite labeled multigraphs and perfect matchings in bipartite tensor products
Ilya I. Bogdanov, Fedor Petrov, Anton Sadovnichiy +1
In 2019, P. Higgins formulated [1] a question about bipartite graphs (see Conjecture 1 below); this question arises in the study of regular finite semigroups. F. V. Petrov formulat…
CayleyPy RL: Pathfinding and Reinforcement Learning on Cayley Graphs
A. Chervov, M. Obozov, A. Soibelman +31
This paper is the second in a series of studies on developing efficient artificial intelligence-based approaches to pathfinding on extremely large graphs (e.g. nodes) wit…
On the rank of the communication matrix for deterministic two-way finite automata
Semyon Petrov, Fedor Petrov, Alexander Okhotin
The communication matrix for two-way deterministic finite automata (2DFA) with states is defined for an automaton over a full alphabet of all possible symbols: its r…
Branching points in the planar Gilbert--Steiner problem have degree 3
Danila Cherkashin, Fedor Petrov
Gilbert--Steiner problem is a generalization of the Steiner tree problem on a specific optimal mass transportation. We show that every branching point in a solution of the planar G…
Combinatorial results implied by many zero divisors in a group ring
Fedor Petrov
It has been recently proved (by Croot, Lev and Pach and the subsequent work by Ellenberg and Gijswijt) that for a group , where is a fixed finite Abeli…
Partitions of nonzero elements of a finite field into pairs
R. N. Karasev, F. V. Petrov
In this paper we prove that the nonzero elements of a finite field with odd characteristic can be partitioned into pairs with prescribed difference (maybe, with some alternatives)…