Integer sequence discovery from small graphs

Hoppe, Travis; Petrone, Anna

doi:10.1016/j.dam.2015.07.017

Cited by 4 publications

(5 citation statements)

References 27 publications

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“…It would be also interesting to study how rope graphs relate to 1-endpoint crossing graphs (Pitler et al, 2013;Kurtz and Kuhlmann, 2017 The languages of encoded graphs have applications to constrained graph enumeration problems. Hoppe and Petrone (Hoppe and Petrone, 2016) have exhaustively enumerated all simple, connected graphs of a finite order and computed a selection of invariants over the sets in order to discover and add 141 new integer sequences to the Online Encyclopedia of Integer Sequences (OEIS). Our previous encoding scheme (Yli-Jyrä and Gómez-Rodríguez, 2017) gave context-free characterisations for some graph properties.…”

Section: Discussionmentioning

confidence: 99%

“…The combination of high parsing speed of transition systems with the accuracy of the attached statistical models have paved the way for practical applications of parsing and similar data transformations enabled by these systems (Yamada and Matsumoto, 2003;Nivre and Scholz, 2004;Zhang and Nivre, 2011;Chen and Manning, 2014;Dyer et al, 2015;Andor et al, 2016;Kiperwasser and Goldberg, 2016;Shi et al, 2017). Transition systems may also be used to encode dependency trees, DAGs and other ordered digraphs, and to connect these to the classical formal language theory and to the problems of graph representation (Turán, 1984;Farzan and Munro, 2013;Yli-Jyrä, 2019), graph enumeration (Pólya, 1937;Conte et al, 2018;Yli-Jyrä, 2019), integer sequence discovery (Hoppe and Petrone, 2016;Yli-Jyrä and Gómez-Rodríguez, 2017), maximum subgraph inference (Conte et al, 2019;Yli-Jyrä and Gómez-Rodríguez, 2017), algebraic representations of graph queries (Courcelle, 1990;Ogawa, 2004;Yli-Jyrä and Gómez-Rodríguez, 2017), encoder-decoder parsing (Vinyals et al, 2015;Strzyz et al, 2019) and parsing as sequence labeling .…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Transition-Based Coding and Formal Language Theory for Ordered Digraphs

Yli-Jyrä¹

2019

Proceedings of the 14th International Conference on Finite-State Methods and Natural Language Processing

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Transition-based parsing of natural language uses transition systems to build directed annotation graphs (digraphs) for sentences. In this paper, we define, for an arbitrary ordered digraph, a unique decomposition and a corresponding linear encoding that are associated bijectively with each other via a new transition system. These results give us an efficient and succinct representation for digraphs and sets of digraphs. Based on the system and our analysis of its syntactic properties, we give structural bounds under which the set of encoded digraphs is restricted and becomes a context-free or a regular string language. The context-free restriction is essentially a superset of the encodings used previously to characterize properties of noncrossing digraphs and to solve maximal subgraphs problems. The regular restriction with a tight bound is shown to capture the Universal Dependencies v2.4 treebanks in linguistics.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transition-Based Coding and Formal Language Theory for Ordered Digraphs

Yli-Jyrä¹

2019

Proceedings of the 14th International Conference on Finite-State Methods and Natural Language Processing

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“…The languages of encoded graphs have applications to constrained graph enumeration problems. Hoppe and Petrone (Hoppe and Petrone, 2016) have exhaustively enumerated all simple, connected graphs of a finite order and computed a selection of invariants over the sets in order to discover and add 141 new integer sequences to the Online Encyclopedia of Integer Sequences (OEIS). Our previous encoding scheme gave context-free characterisations for some graph properties.…”

Section: Discussionmentioning

confidence: 99%

Proceedings of the 14th International Conference on Finite-State Methods and Natural Language Processing

Yli-Jyrä

Kornai

Sakarovitch

et al. 2019

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Context-free graph grammars, in particular hyperedge replacement graph grammars, look back on over 30 years of history. They share many of the good properties of contextfree string languages. Unfortunately, the complexity of parsing is the big exception: early results in the field showed that even for fixed grammars, the membership problem can be NP-complete. Moreover, the known results about polynomial parsing that were obtained afterwards, while constituting nice theoretical work, seemed to be of limited practical value. This is because they were either based on very "impractical" restrictions, or the degree of the polynomial running time depended on the grammar and could thus become large. In the current decade, the question received renewed interest because hyperedge replacement is one of the candidate formalisms for specifying semantic graphs in natural language processing. Using graph grammars in this area requires parsing algorithms that are not only polynomial in theory, but efficient in practice. Preferably, the degree of the polynomial bounding their running time should be a (small) constant independent of the grammar, or else it should depend on parameters not likely to be large. The talk will present an overview of results towards this goal, discussing their requirements, advantages, and disadvantages as well as a few possible directions for future work.

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“…Order In 2014, Hoppe and Petrone [42] exhaustively enumerated all simple, connected graphs of order ≤ 10 using nauty [52] and have computed the independence number, automorphism group size, chromatic number, girth, diameter and various properties like Hamiltonicity and Eulerianness over this set. Integer sequences were constructed from these invariants and checked against the Online Encyclopedia of Integer Sequences (OEIS).…”

Section: Graph Typementioning

confidence: 99%