Effective constructions in well-partially- ordered free monoids

Abstract

For strings υ and w define υ≤w if and only if υ is a scattered substring of w. We give a general solution for a problem of Haines to effectively determine regular expressions for L̃= {w:∃υ ε{lunate} Lυ ≤ w} and L{most positive}={υ:∃w ε{lunate} L υ ≤ w} when L denotes an arbitrary context-free language. We show by an inductive argument that one can effectively determine L̃ and L{most positive} for each language L in the algebraic extension of some family K if and only if one can do so for each language in K. © 1978.