@book{a2d60f72d9c040d89992dad51cc96911,

title = "Generating All Circular Shifts by Context-Free Grammars in Chomsky Normal Form",

abstract = "Let $\{a_1,a_2,\ldots,a_n\}$ be an alphabet of $n$ symbols and let $C_n$ be the language of circular shifts of the word $a_1a_2\cdots a_n$; so $C_n = \{a_1a_2\cdots a_{n-1}a_n, a_2a_3\cdots a_na_1, \ldots,a_na_1\cdots a_{n-2}a_{n-1}\}$. We discuss a few families of context-free grammars $G_n$ ($n\geq 1$) in Chomsky normal form such that $G_n$ generates $C_n$. The grammars in these families are inverstigated with respect to their descriptional complexity, i.e., we determine the number of nonterminal symbols $\nu(n)$ and the number of rules $\pi(n)$ of $G_n$ as functions of $n$. These $\nu$ and $\pi$ 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 $\nu$ and $\pi$ are linear.",

keywords = "IR-53978, circular shift, unambiguous grammar, Chomsky normal form, permutation, Context-free grammar, descriptional complexity, EWI-1880, METIS-227387",

author = "P.R.J. Asveld",

note = "Asveld573:2005 publisher=CTIT, number of pages=40 ",

year = "2005",

language = "Undefined",

series = "CTIT Technical Report Series",

publisher = "Centre for Telematics and Information Technology (CTIT)",

number = "05-23",

address = "Netherlands",

}