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 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.

scholarly journals Greibach Normal Form in Algebraically Complete Semirings

2002 ◽  
Vol 9 (46) ◽  
Author(s):  
Zoltán Ésik ◽  
Hans Leiß
Keyword(s):  
Fixed Point ◽  
Normal Form ◽  
Fixed Points ◽  
Form Theorem ◽  
Point Operator ◽  
Normal Form Theorem ◽  
Context Free ◽  
Greibach Normal Form

We give inequational and equational axioms for semirings with a fixed-point operator and formally develop a fragment of the theory of context-free languages. In particular, we show that Greibach's normal form theorem depends only on a few equational properties of least pre-fixed-points in semirings, and elimination of chain- and deletion rules depend on their inequational properties (and the idempotency of addition). It follows that these normal form theorems also hold in non-continuous semirings having enough fixed-points.

Sign in / Sign up

Export Citation Format

Share Document