TY - BOOK

T1 - Generating All Circular Shifts by Context-Free Grammars in Greibach Normal Form

AU - Asveld, P.R.J.

PY - 2007

Y1 - 2007

N2 - For each alphabet $\Sigma_n=\{a_1,a_2,\ldots,a_n\}$, linearly ordered by $a_1<a_2<\cdots<a_n$, let $C_n$ be the language of circular or cyclic shifts over $\Sigma_n$, i.e., $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 study a few families of context-free grammars $G_n$ ($n\geq1$) in Greibach normal form such that $G_n$ generates $C_n$. The members of these grammar families are investigated with respect to the following descriptional complexity measures: the number of nonterminals $\nu(n)$, the number of rules $\pi(n)$ and the number of leftmost derivations $\delta(n)$ of $G_n$. As in the case of Chomsky normal form, these $\nu$, $\pi$ and $\delta$ are functions bounded by low-degree polynomials. However, the question whether there exists a family of grammars that is minimal with respect to all these measures remains open.

AB - For each alphabet $\Sigma_n=\{a_1,a_2,\ldots,a_n\}$, linearly ordered by $a_1<a_2<\cdots<a_n$, let $C_n$ be the language of circular or cyclic shifts over $\Sigma_n$, i.e., $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 study a few families of context-free grammars $G_n$ ($n\geq1$) in Greibach normal form such that $G_n$ generates $C_n$. The members of these grammar families are investigated with respect to the following descriptional complexity measures: the number of nonterminals $\nu(n)$, the number of rules $\pi(n)$ and the number of leftmost derivations $\delta(n)$ of $G_n$. As in the case of Chomsky normal form, these $\nu$, $\pi$ and $\delta$ are functions bounded by low-degree polynomials. However, the question whether there exists a family of grammars that is minimal with respect to all these measures remains open.

KW - HMI-SLT: Speech and Language Technology

KW - IR-67078

KW - METIS-245697

KW - EWI-9722

M3 - Report

T3 - CTIT Technical Report Series

BT - Generating All Circular Shifts by Context-Free Grammars in Greibach Normal Form

PB - Centre for Telematics and Information Technology (CTIT)

CY - Enschede

ER -