On the context-free production complexity of finite languages
Discrete Applied Mathematics
Concrete Math
Introduction to Formal Language Theory
Introduction to Formal Language Theory
Generating all permutations by context-free grammars in Chomsky normal form
Theoretical Computer Science - Algebraic methods in language processing
Generating all permutations by context-free grammars in Greibach normal form
Theoretical Computer Science
Lower bounds for context-free grammars
Information Processing Letters
Permuting operations on strings and their relation to prime numbers
Discrete Applied Mathematics
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Let {a1, a2,..., an} be an alphabet of n symbols and let Cn be the language of circular or cyclic shifts of the word a1a2 ... an; so Cn = {a1a2 ... an-1an, a2a3 ... ana1, ..., ana1..., an-2an-1}. We discuss a few families of context-free grammars Gn (n ≥ 1) in Chomsky normal form such that Gn generates Cn. The grammars in these families are investigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols ν(n) and the number of rules π(n) of Gn as functions of n. These ν and π happen to be functions bounded by low-degree polynomials, particularly when we focus our attention to unambiguous grammars. Finally, we introduce a family of minimal unambiguous grammars for which ν and π are linear.