On Finite-Index Indexed Grammars and Their Restrictions
  The family, L(INDLIN), of languages generated by linear indexed grammars has been studied in the literature. It is known that the Parikh image of every language in L(INDLIN) is semi-linear. However, there are bounded semi linear languages that are not in L(INDLIN). Here, we look at larger families of (restricted) indexed languages and study their properties, their relationships, and their decidability properties. 
Flavio D'Alessandro, Oscar H. Ibarra, Ian McQuillan
cs.FL