Positional queuetions
In this work, we consider properties of VCG and GSP positional auctions in queues. The work is a continuation of "Position Auctions for Sponsored Search in Marketplaces" by the same author.
cs.GT↗
arXiv subjects
Vladimir Yankovskiy
Publications and source records attributed to Vladimir Yankovskiy.
Isometry groups of formal languages for generalized Levenshtein distances
This article is a partial answer to the question of which groups can be represented as isometry groups of formal languages for generalized Levenshtein distances. Namely, it is proved that for any language the modulus of the difference between the lengths of its words and the lengths of their images under isometry for an arbitrary generalized Levenshtein distance that satisfies the condition that the weight of the replacement operation is less than twice the weight of the removal operation is bounded above by a constant that depends only on the language itself. From this, in particular, it follows that the isometry groups of formal languages with respect to such metrics always embed into the group $Π_{n=1}^\infty S_{n}$. We also construct a number of examples showing that this estimate is, in a certain sense, unimprovable.
math.GR↗
Groups with context-free Diophantine problem
We find algebraic conditions on a group equivalent to the position of its Diophantine problem in the Chomsky Hierarchy. In particular, we prove that a finitely generated group has a context-free Diophantine problem if and only if it is finite.
math.GR↗