On Shuffling a Word with its Letter-to-Letter Substitution

Abstract

Denote by ш the operation of interleaving, or shuffling, of words. We prove that, given a regular language R and a letter-to-letter morphism φ, it is undecidable whether or not there exists a word ω such that ω ш φ(ω) ∩ R ≠ ø.