Algorithms for determining relative inclusion star height and inclusion star height

Abstract

Let C=(R 1,⋯,R m) be a finite class of regular languages over a finite alphabet Σ. Let Δ=( b 1,⋯, b m ) be an alphabet, and δ be the substitution from Δ ∗ into Σ ∗ such that δb i )= R i for all i. Let R 10,R 20⊂Σ ∗ be two regular languages. The relative inclusion star height h r(R 10,R 20, C) of (R 10,R 20) w.r.t. C is the minimum star height of regular languages L⊂Δ ∗ such that R 10⊂ δ( L)⊂ R 20. This paper proves the existence of an algorithm for determining relative inclusion star height.