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Uniform Parsing for Hyperedge Replacement 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)ORCID iD: 0000-0001-7349-7693
Umeå University, Faculty of Science and Technology, Department of Computing Science. (Foundations of Language Processing)ORCID iD: 0000-0002-8722-5661
Faculty of Computer Science, TU Dresden.
2018 (English)Report (Other academic)
Abstract [en]

It is well known that hyperedge-replacement grammars can generate NP-complete graph languages even under seemingly harsh restrictions. This means that the parsing problem is difficult even in the non-uniform setting, in which the grammar is considered to be fixed rather than being part of the input. Little is known about restrictions under which truly uniform polynomial parsing is possible. In this paper we propose a low-degree polynomial-time algorithm that solves the uniform parsing problem for a restricted type of hyperedge-replacement grammars which we expect to be of interest for practical applications.

Place, publisher, year, edition, pages
Umeå: Umeå universitet , 2018. , p. 21
Series
Report / UMINF, ISSN 0348-0542 ; 18.13
Keywords [en]
graph grammars, hyperedge replacement, order-preserving graph grammars, uniform parsing problem
National Category
Computer Sciences
Research subject
Computing Science
Identifiers
URN: urn:nbn:se:umu:diva-153384OAI: oai:DiVA.org:umu-153384DiVA, id: diva2:1264041
Available from: 2018-11-19 Created: 2018-11-19 Last updated: 2019-01-07Bibliographically 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: 2019-01-11Bibliographically approved

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Björklund, HenrikDrewes, FrankEricson, PetterStarke, Florian
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