scholarly journals Some Combinatorial Arrays Related to the Lotka-Volterra System

10.37236/4413 ◽  
2015 ◽  
Vol 22 (2) ◽  
Author(s):  
David Callan ◽  
Shi-Mei Ma ◽  
Toufik Mansour
Keyword(s):  
Stirling Numbers ◽  
Volterra System ◽  
Eulerian Numbers ◽  
Context Free ◽  
Context Free Grammars

The purpose of this paper is to investigate several context-free grammars suggested by the Lotka-Volterra system. Some combinatorial arrays, involving the Stirling numbers of the second kind and Eulerian numbers, are generated by these context-free grammars. In particular, we present grammatical characterization of some statistics on cyclically ordered partitions.

ON THE LEFTMOST DERVIATION IN MATRIX GRAMMARS

1999 ◽  
Vol 10 (01) ◽  
pp. 61-79 ◽  
Author(s):  
JÜRGEN DASSOW ◽  
HENNING FERNAU ◽  
GHEORGHE PĂUN
Keyword(s):  
Systematic Study ◽  
Regular Language ◽  
Formal Languages ◽  
Open Problems ◽  
Recursively Enumerable ◽  
Leftmost Derivation ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

Matrix grammars are one of the classical topics of formal languages, more specifically, regulated rewriting. Although this type of control on the work of context-free grammars is one of the earliest, matrix grammars still raise interesting questions (not to speak about old open problems in this area). One such class of problems concerns the leftmost derivation (in grammars without appearance checking). The main point of this paper is the systematic study of all possibilities of defining leftmost derivation in matrix grammars. Twelve types of such a restriction are defined, only four of which being discussed in literature. For seven of them, we find a proof of a characterization of recursively enumerable languages (by matrix grammars with arbitrary context-free rules but without appearance checking). Other three cases characterize the recursively enumerable languages modulo a morphism and an intersection with a regular language. In this way, we solve nearly all problems listed as open on page 67 of the monograph [7], which can be seen as the main contribution of this paper. Moreover, we find a characterization of the recursively enumerable languages for matrix grammars with the leftmost restriction defined on classes of a given partition of the nonterminal alphabet.

scholarly journals Analyzing Ambiguity of Context-Free Grammars

2006 ◽  
Vol 13 (9) ◽  
Author(s):  
Claus Brabrand ◽  
Robert Giegerich ◽  
Anders Møller
Keyword(s):  
Static Analysis ◽  
Real World ◽  
Full Text ◽  
Language Design ◽  
Rna Analysis ◽  
Parser Generation ◽  
Context Free ◽  
Linguistic Characterization ◽  
Context Free Grammars

<p>It has been known since 1962 that the ambiguity problem for context-free grammars is undecidable. Ambiguity in context-free grammars is a recurring problem in language design and parser generation, as well as in applications where grammars are used as models of real-world physical structures. However, the fact that the problem is undecidable does not mean that there are no useful <em>approximations</em> to the problem.<br /> <br />We observe that there is a simple linguistic characterization of the grammar ambiguity problem, and we show how to exploit this to conservatively approximate the problem based on local regular approximations and grammar unfoldings. As an application, we consider grammars that occur in RNA analysis in bioinformatics, and we demonstrate that our static analysis of context-free grammars is sufficiently precise and efficient to be practically useful.</p><p> </p><p>Full text: <a href="http://dx.doi.org/10.1016/j.scico.2009.11.002" target="_self">http://dx.doi.org/10.1016/j.scico.2009.11.002</a></p>

scholarly journals Analyzing Ambiguity of Context-Free Grammars

2007 ◽  
Vol 14 (10) ◽  
Author(s):  
Claus Brabrand ◽  
Robert Giegerich ◽  
Anders Møller
Keyword(s):  
Static Analysis ◽  
Real World ◽  
Language Design ◽  
Rna Analysis ◽  
Parser Generation ◽  
Context Free ◽  
Linguistic Characterization ◽  
Context Free Grammars

It has been known since 1962 that the ambiguity problem for context-free grammars is undecidable. Ambiguity in context-free grammars is a recurring problem in language design and parser generation, as well as in applications where grammars are used as models of real-world physical structures.<br /> <br />We observe that there is a simple linguistic characterization of the grammar ambiguity problem, and we show how to exploit this to conservatively approximate the problem based on local regular approximations and grammar unfoldings. As an application, we consider grammars that occur in RNA analysis in bioinformatics, and we demonstrate that our static analysis of context-free grammars is sufficiently precise and efficient to be practically useful.

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