On infinite words generated by polynomial D0L systems

We study infinite words generated by polynomially bounded D0L systems and the relations between equivalent and ω-equivalent D0L systems. As the main result we show that if two polynomially bounded D0L systems Gi=(X,hi,w), i=1,2, are ω-equivalent, then there exist an integer t⩾0 and t-tuples (i1,…,it), (j1,…,jt) such that the systems H1=(X,h1hi1…hit,w) and H2=(X,h2hj1…hjt,w) are nearly equivalent in the sense that they generate the same word sequences if certain suffixes of restricted lengths are disregarded.