The number of S-precomplete classes in the functional system P κ τ

Abstract

The problem on the number of precomplete classes in the functional system Pκτ is considered, elements of Pκτ are deterministic S-functions defined on words of length τ composed from letters of an alphabet of cardinality κ. An asymptotics for the number of S-precomplete classes in Pκτ is obtained for arbitrary fixed κ and τ tending to infinity.