scholarly journals Generating all permutations by context-free grammars in Greibach normal form

2008 ◽  
Vol 409 (3) ◽  
pp. 565-577 ◽  
Author(s):  
Peter R.J. Asveld
Keyword(s):  
Normal Form ◽  
Context Free ◽  
Greibach Normal Form ◽  
Context Free Grammars

scholarly journals GENERATING ALL CIRCULAR SHIFTS BY CONTEXT-FREE GRAMMARS IN GREIBACH NORMAL FORM

2007 ◽  
Vol 18 (06) ◽  
pp. 1139-1149 ◽  
Author(s):  
PETER R. J. ASVELD
Keyword(s):  
Normal Form ◽  
Complexity Measures ◽  
Descriptional Complexity ◽  
Low Degree ◽  
Cyclic Shifts ◽  
Low Degree Polynomials ◽  
Context Free ◽  
Greibach Normal Form ◽  
Context Free Grammars

For each alphabet Σn = {a1,a2,…,an}, linearly ordered by a1 < a2 < ⋯ < an, let Cn be the language of circular or cyclic shifts over Σn, i.e., Cn = {a1a2 ⋯ an-1an, a2a3 ⋯ ana1,…,ana1 ⋯ an-2an-1}. We study a few families of context-free grammars Gn (n ≥1) in Greibach normal form such that Gn generates Cn. The members of these grammar families are investigated with respect to the following descriptional complexity measures: the number of nonterminals ν(n), the number of rules π(n) and the number of leftmost derivations δ(n) of Gn. As in the case of Chomsky normal form, these ν, π and δ are functions bounded by low-degree polynomials. However, the question whether there exists a family of grammars that is minimal w. r. t. all these measures remains open.

A Survey of Normal form Covers for Regular Grammars

1981 ◽  
Vol 4 (4) ◽  
pp. 761-776
Author(s):  
Anton Nijholt
Keyword(s):  
Normal Form ◽  
Special Form ◽  
Normal Forms ◽  
Context Free Grammar ◽  
Left Regular ◽  
Regular Grammar ◽  
Left And Right ◽  
Context Free ◽  
Greibach Normal Form

An overview is given of cover results for normal forms of regular grammars. Due to the special form of regular grammars and due to the results which are obtained it is sufficient to consider covering grammars in Greibach normal form. Among other things it is proved that any left-regular grammar can be left covered with a context-free grammar in Greibach normal form. All the cover results concerning the left- and right-regular grammars are listed, with respect to several types of covers, in a cover table.

scholarly journals Normal form algorithms for extended context-free grammars

2001 ◽  
Vol 267 (1-2) ◽  
pp. 35-47 ◽  
Author(s):  
Jürgen Albert ◽  
Dora Giammarresi ◽  
Derick Wood
Keyword(s):  
Normal Form ◽  
Context Free ◽  
Context Free Grammars
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