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Minimisation and Characterisation of Order-Preserving DAG Grammars
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Foundations of Language Processing)ORCID iD: 0000-0002-4696-9787
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Foundations of Language Processing)
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Foundations of Language Processing)ORCID iD: 0000-0002-8722-5661
2018 (English)Report (Other academic)
Abstract [en]

Order-preserving DAG grammars (OPDGs) is a formalism for processing semantic infor- mation in natural languages [5, 4]. OPDGs are sufficiently expressive to model abstract meaning representations, a graph-based form of semantic representation in which nodes en- code objects and edges relations. At the same time, they allow for efficient parsing in the uniform setting, where both the grammar and subject graph are taken as part of the input.

In this article, we introduce an initial algebra semantic for OPDGs, which allows us to view them as regular tree grammars. This makes it possible to transfer a number of results from that domain to OPDGs, both in the unweighted and the weighted case. In particular, we show that deterministic OPDGs can be minimised efficiently, and that they are learnable in the so-called MAT setting. To conclude, we show that the languages generated by OPDGs are MSO-definable.

Place, publisher, year, edition, pages
Umeå: Umeå University , 2018. , p. 19
Series
Report / UMINF, ISSN 0348-0542 ; 18.15
Keywords [en]
graph grammars, minimally adequate teacher, order preservation, weighted graph grammars, weighted learning
National Category
Computer Sciences
Research subject
business data processing
Identifiers
URN: urn:nbn:se:umu:diva-153394OAI: oai:DiVA.org:umu-153394DiVA, id: diva2:1264053
Available from: 2018-11-19 Created: 2018-11-19 Last updated: 2019-07-05Bibliographically approved
In thesis
1. Order-preserving graph grammars
Open this publication in new window or tab >>Order-preserving graph grammars
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Ordningsbevarande grafgrammatiker
Abstract [en]

The field of semantic modelling concerns formal models for semantics, that is, formal structures for the computational and algorithmic processing of meaning. This thesis concerns formal graph languages motivated by this field. In particular, we investigate two formalisms: Order-Preserving DAG Grammars (OPDG) and Order-Preserving Hyperedge Replacement Grammars (OPHG), where OPHG generalise OPDG.

Graph parsing is the practise of, given a graph grammar and a graph, to determine if, and in which way, the grammar could have generated the graph. If the grammar is considered fixed, it is the non-uniform graph parsing problem, while if the grammars is considered part of the input, it is named the uniform graph parsing problem. Most graph grammars have parsing problems known to be NP-complete, or even exponential, even in the non-uniform case. We show both OPDG and OPHG to have polynomial uniform parsing problems, under certain assumptions.

We also show these parsing algorithms to be suitable, not just for determining membership in graph languages, but for computing weights of graphs in graph series.

Additionally, OPDG is shown to have several properties common to regular languages, such as MSO definability and MAT learnability. We moreover show a direct corresponcence between OPDG and the regular tree grammars.

Finally, we present some limited practical experiments showing that real-world semantic graphs appear to mostly conform to the requirements set by OPDG, after minimal, reversible processing.

Place, publisher, year, edition, pages
Umeå: Umeå universitet, Institutionen för datavetenskap, 2019. p. 56
Series
Report / UMINF, ISSN 0348-0542 ; 19.01
Keywords
Graph grammars, graph parsing, graph series, hyperedge replacement, uniform parsing problem, abstract meaning representation, semantic modelling, order preservation, reentrancy preservation, minimally adequate teacher, weighted graph grammars
National Category
Computer Sciences
Identifiers
urn:nbn:se:umu:diva-154777 (URN)978-91-7855-017-3 (ISBN)
Public defence
2019-02-04, MA121, Umeå, 13:00 (English)
Opponent
Supervisors
Available from: 2019-01-14 Created: 2019-01-07 Last updated: 2019-07-05Bibliographically approved

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Björklund, HenrikBjörklund, JohannaEricson, Petter

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