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Lambek Grammars, Tree Adjoining Grammars and Hyperedge Replacement Grammars

Richard Moot
2008 International Workshop on Tree Adjoining Grammars and Related Formalisms  
generating) hyperedge replacement grammars as an intermediate step.  ...  Two recent extension of the nonassociative Lambek calculus, the Lambek-Grishin calculus and the multimodal Lambek calculus, are shown to generate class of languages as tree adjoining grammars, using (tree  ...  Tree Adjoining Grammars and Hyperedge Replacement Grammars Tree Adjoining Grammars (Joshi and Schabes, 1997) combine trees using the operations of substitution (shown in Figure 1 ) which replaces a  ... 
dblp:conf/tag/Moot08 fatcat:7lzl7olsszghblld3ccjqpah3u

Hyperedge replacement jungle rewriting for term-rewriting systems and logic programming

Andrea Corradini, Francesca Rossi
1993 Theoretical Computer Science  
Introduction In this paper we investigate the properties of hyperedge replacement jungle rewriting, a formalism based on graph rewriting, and demonstrate its expressive power, showing that it can model  ...  Rossi, Hyperedge replacement jungle rewriting for term-rewriting systems and logic programming, Theoretical Computer Science 109 (1993) 7-48.  ...  Both [lS] and [3] define the basic notion of hyperedge replacement (called graph substitution in [3]) in a set-theoretic way, and then they prove that it can be formulated equivalently as a double  ... 
doi:10.1016/0304-3975(93)90063-y fatcat:yok3r5si5fdqdh4y5foa7yvsem

Graph Algebras for Bigraphs

Davide Grohmann, Marino Miculan
2010 Electronic Communications of the EASST  
Moreover, we give a formal connection between these languages and Synchronized Hyperedge Replacement algebras and the hierarchical graphs used in Architectural Design Rewriting.  ...  In this paper we present an algebra of typed graph terms which correspond precisely to binding bigraphs over a given signature.  ...  We denote by l( x) atomic hyperedges whose tentacles are linked to the names in x, whilst by L( x)[A\ y] non-atomic hyperedges having exiting tentacles linked to the names in x, containing a subgraph A  ... 
doi:10.14279/tuj.eceasst.29.414 dblp:journals/eceasst/GrohmannM10 fatcat:tzyctdq5tfemfop5dyoi264vpa

Molecular Hypergraph Grammar with its Application to Molecular Optimization [article]

Hiroshi Kajino
2019 arXiv   pre-print
Two fundamental challenges are: (i) it is not trivial to generate valid molecules in a controllable way due to hard chemical constraints such as the valency conditions, and (ii) it is often costly to evaluate  ...  D Basic Statistics of MHG This section reports basic statistics of MHG inferred using the ZINC dataset.  ...  We also investigate the coverage rate of the language associated with MHG (i.e., how many molecules out of all possible molecules can MHG represent?).  ... 
arXiv:1809.02745v2 fatcat:x3y6n472ybdufe7xvuzb5iuihy

HYPEREDGE REPLACEMENT GRAPH GRAMMARS [chapter]

F. DREWES, H.-J. KREOWSKI, A. HABEL
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.  ...  The work presented here has been supported by ESPRIT Basic Research Working Group 7183 (COMPUGRAPH II).  ... 
doi:10.1142/9789812384720_0002 fatcat:snksvj3gnfavxmy5ff4732mpnu

Decidable boundedness problems for hyperedge-replacement graph grammars [chapter]

Annegret Habel, Hans-Jörg Kreowski, Walter Vogler
1989 Lecture Notes in Computer Science  
Consider a class C of hyperedge--replacement graph grammars and a numeric function on graphs like the number of edges, the degree (i.e., the maximum of the degrees of all nodes of a graph), the number  ...  Each such function induces a Boundedness Problem for the class C: Given a grammar HRG in C, are the function values of all graphs in the language L(HRG), generated by HRG, bounded by an integer or not?  ...  Definition (hyperedge-replacement grammars and languages) 1.  ... 
doi:10.1007/3-540-50939-9_138 fatcat:leulgcna3jhj3lwwkjofyxpq44

Semantic Hypergraphs [article]

Telmo Menezes, Camille Roth
2021 arXiv   pre-print
We define a pattern language representable in SH itself, and a process to discover knowledge inference rules.  ...  Approaches to Natural language processing (NLP) may be classified along a double dichotomy open/opaque - strict/adaptive.  ...  In a sense, these are replacement rules, except that the original hyperedge is preserved.  ... 
arXiv:1908.10784v2 fatcat:mpf3qtkst5hldbyrvpvcx4vtnu

HyperGraphDB: A Generalized Graph Database [chapter]

Borislav Iordanov
2010 Lecture Notes in Computer Science  
and natural language processing.  ...  We present HyperGraphDB, a novel graph database based on generalized hypergraphs where hyperedges can contain other hyperedges.  ...  In the HyperGraphDB data model, the basic representational unit is called an atom. Each atom has an associated tuple of atoms called its target set.  ... 
doi:10.1007/978-3-642-16720-1_3 fatcat:amjp33re6zbsjhowb6wn72or5a

Various interplays between relation and cylindric algebras [article]

Tarek Sayed Ahmed
2013 arXiv   pre-print
Our results apply to many cylindric-like algebras, including Pinter's substitution algebras and Halmos' polyadic algebras with and without equality.  ...  The techniques used are essentially those used by Hirsch and Hodkinson, and later by Hirsch in hh and r. In fact, the main result in hh follows from our more general construction.  ...  We call such hyperedges atomic hyperedges.  ... 
arXiv:1305.5269v1 fatcat:cxeu6zqwgjfd5evo3i4cybij6u

Tarzan: Communicating and Moving in Wireless Jungles

Emilio Tuosto
2005 Electronical Notes in Theoretical Computer Science  
Figure 1 aims at giving an intuition of hyperedge replacement.  ...  Mobility has been recently considered in [9, 10, 6, 16] where synchronised hyperedge replacement (SHR) has been investigated.  ... 
doi:10.1016/j.entcs.2004.01.022 fatcat:wv7ue3pzszegrlqgvx3hkjlllq

Decidable boundedness problems for sets of graphs generated by hyperedge-replacement

Annegret Habel, Hans-Jörg Kreowski, Walter Vogler
1991 Theoretical Computer Science  
Decidable boundedness problems for hyperedge-replacement graphs  ...  Vogler, Decidable boundedness problems for sets of graphs generated by hyperedge-replacement, Theoretical Computer Science 89 (1991) 33-62.  ...  Now we are ready to introduce how hypergraphs may substitute hyperedges. An (m, n)-edge can be replaced by an (m, n)-hypergraph in two steps. (1) Remove the hyperedge.  ... 
doi:10.1016/0304-3975(90)90106-r fatcat:sw6fgczejzhq3fg5gn6m2nmbku

Forest Automata for Verification of Heap Manipulation [chapter]

Peter Habermehl, Lukáš Holík, Adam Rogalewicz, Jiří Šimáček, Tomáš Vojnar
2011 Lecture Notes in Computer Science  
The substitution is similar to an ordinary hyperedge replacement used in graph grammars.  ...  If H is of level j > 0, then hypergraphs from H are obtained in such a way that hyperedges labelled by boxes B ∈ Γ j are substituted in all possible ways by plain components from B .  ... 
doi:10.1007/978-3-642-22110-1_34 fatcat:sqqgmi4dg5b4vbavnubexz553e

Forest automata for verification of heap manipulation

Peter Habermehl, Lukáš Holík, Adam Rogalewicz, Jiří Šimáček, Tomáš Vojnar
2012 Formal methods in system design  
The substitution is similar to an ordinary hyperedge replacement used in graph grammars.  ...  If H is of level j > 0, then hypergraphs from H are obtained in such a way that hyperedges labelled by boxes B ∈ Γ j are substituted in all possible ways by plain components from B .  ... 
doi:10.1007/s10703-012-0150-8 fatcat:fxh3cobsojgpjliwunjegwzqay

Strongly representable atom structures and neat embeddings [article]

Tarek Sayed Ahmed, Mohammed Khaled
2013 arXiv   pre-print
Finally we devise what we call neat games, for such a game if \pe\ has a \ws \ on an atomic algebra \A in certain atomic game and \pa has a \ws in another atomic game, then such algebras are elementary  ...  In this paper we give an alternative construction using Monk like algebras that are binary generated to show that the class of strongly representable atom structures is not elementary.  ...  In this case omitting types theorems holds for countable languages and atomic theories have atomic models. Here all substitutions corresponding to bijective maps are definable.  ... 
arXiv:1307.4298v1 fatcat:q66oeqpnlzdjto7rrq5rivudgi

A Synchronous Hyperedge Replacement Grammar based approach for AMR parsing

Xiaochang Peng, Linfeng Song, Daniel Gildea
2015 Proceedings of the Nineteenth Conference on Computational Natural Language Learning  
We apply Markov Chain Monte Carlo (MCMC) algorithms to learn Synchronous Hyperedge Replacement Grammar (SHRG) rules from a forest that represents likely derivations consistent with a fixed string-to-graph  ...  We also show some useful strategies to overcome existing problems in an SHRG-based parser and present preliminary results of a graph-grammar-based approach.  ...  While CFG generates natural language strings by successively rewriting nonterminal tokens, the nonterminals in HRG are hyperedges, and each rewriting step in HRG replaces a hyperedge nonterminal with a  ... 
doi:10.18653/v1/k15-1004 dblp:conf/conll/PengSG15 fatcat:cal7cudlardmfg275r6mrwgefi
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