Size complexity in context-free grammars forms

Abstract

Grammar forms are compared for their efficiency in representing languages, as measured by the sizes (i.e. total number of symbols, number of variable occurrences, number of productions, and number of distinct variables) of interpretation grammars. For every regular set, right- and left-linear forms are essentially equal in efficiency. Any form for the regular sets provides, at most, polynomial improvement over right-linear form. Moreover, any polynomial improvement is attained by some such form, at least on certain languages. Greater improvement for some languages is possible using forms expressing larger classes of languages than the regular sets. However, there are some languages for which no improvement over right-linear form is possible. While a similar set of results holds for forms expressing exactly the linear languages, only linear improvement can occur for forms expressing all the context-free languages.