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Page 5769 of Mathematical Reviews Vol. , Issue 2000h [page]

2000 Mathematical Reviews  
The proof relies heavily on the use of elementary morphisms in a power series framework and also gives a new method for deciding whether or not a given DOL language is context-free.” 68Q Theory of computing  ...  For grammars generating hypergraphs there are two well-known models, the context-free hypergraph (CFHG) grammars by Boud- eron and Courcelle and by Habel et al., which replace a hyper- edge by a hypergraph  ... 

Page 3353 of Mathematical Reviews Vol. , Issue 2001E [page]

2001 Mathematical Reviews  
{For the entire collection see MR 2001d:68006. } 2001€:68093 68Q42 68R10 Klempien-Hinrichs, Renate (D-BRMN; Bremen) The generative power of context-free node rewriting in hypergraphs.  ...  Summary: “Context-free hypergraph grammars allow the defini- tion of sets of hypergraphs in a recursive way.  ... 

HRNCE grammars — a hypergraph generating system with an eNCE way of rewriting

Changwook Kim, Tae Eui Jeong
1999 Theoretical Computer Science  
., a hyperedge together with its incident nodes) by a hypergraph, whose nodes are connected to (or contained in) the hyperedges surrounding the replaced handle by using the eNCE rewriting mechanism.  ...  We introduce a hypergraph-generating system, called HRNCE grammars, which is structurally simple and descriptively powerful.  ...  the definition of context-free rewriting systems given in [5] .  ... 
doi:10.1016/s0304-3975(99)00258-3 fatcat:7kulb5wykzegbhonizj5ol6jg4

Page 2882 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
They provide the most powerful class of context-free hypergraph grammars known to date. In this article a very natural restriction, the so-called remote-free C-hNCE grammar, is studied.  ...  {For the entire collection see MR 2003b:68007.} 2003d:68123 68Q42 Klempien-Hinrichs, Renate (D-BRMN; Bremen) Normal forms for context-free node-rewriting hypergraph grammars.  ... 

Page 5380 of Mathematical Reviews Vol. , Issue 94i [page]

1994 Mathematical Reviews  
This generalizes the dou- ble Greibach normal form of context-free grammars. Moreover, it provides a natural grammatical characterization of the context- free hypergraph languages of bounded degree.  ...  In order to increase generative power, hyperedge-rewriting grammars have been introduced in the litera- ture.  ... 

Context-free hypergraph grammars have the same term-generating power as attribute grammars

Joost Engelfriet, Linda Heyker
1992 Acta Informatica  
Context-free hypergraph grammars and attribute grammars generate the same class of term languages.  ...  Extending the context-free hypergraph grammar with a context-free grammar and a semantic domain, a syntax-directed translation device is obtained that is equivalent to the attribute grammar.  ...  The authors wish to thank George Leih for several useful observations. The remarks of the referees have been very helpful in writing the conclusion.  ... 
doi:10.1007/bf01178504 fatcat:spgr3hfupzdchnqlxopuf6wnru

String Diagram Rewrite Theory I: Rewriting with Frobenius Structure [article]

Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Pawel Sobocinski, Fabio Zanasi
2022 arXiv   pre-print
Our work introduces a combinatorial interpretation of string diagram rewriting modulo Frobenius structures, in terms of double-pushout hypergraph rewriting.  ...  String diagrams are a powerful and intuitive graphical syntax, originated in the study of symmetric monoidal categories.  ...  We are thankful to the anonymous referees for their helpful comments; Fabio  ... 
arXiv:2012.01847v2 fatcat:5defrofqqrhm7aiqtzb4pkywfi

Rewriting in Free Hypergraph Categories

Fabio Zanasi
2017 Electronic Proceedings in Theoretical Computer Science  
We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object.  ...  This interpretation allows to use results on hypergraphs to ensure decidability of confluence for rewriting in a free hypergraph category.  ...  Acknowledgements Thanks to Filippo Bonchi, Brendan Fong, Fabio Gadducci, Aleks Kissinger, the GAM participants and referees for useful comments and discussion on the topics of this paper.  ... 
doi:10.4204/eptcs.263.2 fatcat:meiolnyhvfhafci7ymy65jjmle

Parallel Communicating String - Graph P System

Meena Parvathy Sankar, N.G. David
2011 Mapana Journal of Sciences  
The concept of parallel communicating grammar systems generating string languages is extended to string-graph P systems and their generative power is studied.  ...  It is also established that for every language L generated by a parallel communicating grammar system there exists an equivalent parallel communicating string-graph P system generating the string-graph  ...  of context free evolution rules.  ... 
doi:10.12723/mjs.19.6 fatcat:p6hjmtcbanhc5otsglzz5usuay

Rewriting modulo symmetric monoidal structure

Filippo Bonchi, Fabio Gadducci, Aleks Kissinger, Paweł Sobociński, Fabio Zanasi
2016 Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science - LICS '16  
This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure  ...  We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting  ...  More precisely, a DPO system on hypergraphs of type Σ amounts to a rewriting system on the free SMC generated by Σ together with a chosen special Frobenius structure.  ... 
doi:10.1145/2933575.2935316 dblp:conf/lics/BonchiGKSZ16 fatcat:t3t4tv7junagbmmmw3lfv5hp3y


1997 Handbook of Graph Grammars and Computing by Graph Transformation  
In this survey the concept of hyperedge replacement is presented as an elementary approach to graph and hypergraph generation.  ...  In particular, hyperedge replacement graph grammars are discussed as a (hyper)graph-grammatical counterpart to context-free string grammars.  ...  Acknowledgement We thank Grzegorz Rozenberg and the anonymous referee for helpful comments on a draft of this chapter.  ... 
doi:10.1142/9789812384720_0002 fatcat:snksvj3gnfavxmy5ff4732mpnu

Hypergraph languages of bounded degree

Joost Engelfriet, Linda Heyker
1994 Journal of computer and system sciences (Print)  
Two types of hypergraph rewriting grammar are considered: the well-known context-free hypergraph grammar (or CFHG grammar, also known as hyperedge replacement system or HR system) and tile more recent  ...  This implies that these two types of grammar generate the same class of graph languages of bounded degree, but incomparable classes of hypergraph languages.  ...  The main power that S-HH grammars have in addition to context-free hypergraph grammars is duplication.  ... 
doi:10.1016/s0022-0000(05)80022-4 fatcat:h7qp4muenjbgpaj32fnzcb6qbe

Tree Transducers and Tree Compressions [chapter]

Sebastian Maneth, Giorgio Busatto
2004 Lecture Notes in Computer Science  
A more powerful way of tree compression is to allow the sharing of tree patterns, i.e., internal parts of the tree.  ...  The main result is that a sharing graph representation of the corresponding output tree can be computed in time linear in the size of s.  ...  The first author is grateful to Markus Lohrey for providing many useful references, and in particular for the introduction to the concept of sharing graphs.  ... 
doi:10.1007/978-3-540-24727-2_26 fatcat:7tzr7rrdyjf5lny7i2pdzilyqq

On the Decidability Status of Reachability and Coverability in Graph Transformation Systems

Nathalie Bertrand, Giorgio Delzanno, Barbara König, Arnaud Sangnier, Jan Stückrath, Marc Herbstritt
2012 International Conference on Rewriting Techniques and Applications  
In this paper we reformulate results obtained, e.g., for context-free graph grammars and concurrency models, such as Petri nets, in the more general setting of graph transformation systems and study new  ...  The former is a fundamental problem for any computational model, the latter is strictly related to verification of safety properties in which the pattern specifies an infinite set of bad configurations  ...  Acknowledgements: We would like to thank Roland Meyer for interesting discussions about several aspects of this work.  ... 
doi:10.4230/lipics.rta.2012.101 dblp:conf/rta/BertrandDKSS12 fatcat:62mssb5jebadxaiw7ojdlp2c7e

Relational data base design using refinement rules

C. Batini, A. d'Atri
1983 RAIRO Informatique théorique  
In the hypergraph formalism we need a concept of (context free) rewriting rule and hypergraph grammar to characterize top-down schema génération.  ...  In fact in its full generality the problem is complex and cannot be solved in the framework of context free grammars. We say that HeJf?  ... 
doi:10.1051/ita/1983170200971 fatcat:rovp5nli5zepxah264zls45fle
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