On Finite-Index Indexed Grammars and Their Restrictions
Flavio D'Alessandro, Oscar H. Ibarra, Ian McQuillan
TL;DR
This paper explores larger classes of restricted indexed languages, examining their properties, relationships, and decidability, expanding understanding beyond linear indexed grammars.
Contribution
It introduces and analyzes new families of restricted indexed languages, detailing their properties, relationships, and decidability aspects beyond linear indexed grammars.
Findings
L(INDLIN) languages have semi-linear Parikh images.
Some bounded semi-linear languages are not in L(INDLIN).
New families of restricted indexed languages are characterized and compared.
Abstract
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.
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