Treewidth, pathwidth and cospan decompositions with applications to graph-accepting tree automata

Blume, Christoph; Bruggink, H. J. Sander; Friedrich, Martin; König, Barbara

doi:10.1016/j.jvlc.2012.10.002

Cited by 11 publications

(13 citation statements)

References 20 publications

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“…[13,6,4]). The originality of our approach consists in restricting to the category of unambiguous graphs and connecting morphisms that allow the resulting semigroup to be an inverse semigroup.…”

Section: Resultsmentioning

confidence: 99%

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Inverse Monoids of Higher-Dimensional Strings

Janin

2015

Theoretical Aspects of Computing - ICTAC 2015

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Abstract.Halfway between graph transformation theory and inverse semigroup theory, we define higher dimensional strings as bi-deterministic graphs with distinguished sets of input roots and output roots. We show that these generalized strings can be equipped with an associative product so that the resulting algebraic structure is an inverse semigroup. Its natural order is shown to capture existence of root preserving graph morphism. A simple set of generators is characterized. As a subsemigroup example, we show how all finite grids are finitely generated. Finally, simple additional restrictions on products lead to the definition of subclasses with decidable Monadic Second Order (MSO) language theory.

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Section: Resultsmentioning

confidence: 99%

“…In category theoretical term, a birooted graph is a cospan (see for instance [4]). The existence of pushouts in the category UCGrph(A) allows us to define the product of birooted graphs as the product of their cospan.…”

Section: Remarkmentioning

confidence: 99%

Inverse Monoids of Higher-Dimensional Strings

Janin

2015

Theoretical Aspects of Computing - ICTAC 2015

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“…By virtue of this algebraic structure we introduced a syntactic recognizability notion for sets of fuzzy graphs employing the syntactic magmoid in a role analogous to the syntactic monoid of string languages. This approach shall allow us to explore the fuzzy case for existing crisp graph theoretic methods and techniques involving formal verification [3,4,13] and natural language processing [31] as well as for the syntactic complexity of string and graph languages [14,15,22].…”

Section: Resultsmentioning

confidence: 99%

Fuzzy graphs: algebraic structure and syntactic recognition

et al. 2013

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“…With respect to any such fixed representation, learners for strings or trees can be also seen as learners for other structures. For instance, representations of graphs and multigraphs by trees or strings are described in [29,79].…”

Section: Beyond Treesmentioning

confidence: 99%

Learning Tree Languages

Björklund

Fernau

2016

Topics in Grammatical Inference

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Tree languages have proved to be a versatile and rewarding extension of the classical notion of string languages. Many nice applications have been established over the years, in areas such as Natural Language Processing, Information Extraction, and Computational Biology. Although some properties of string languages transfer easily to the tree case, in particular for regular languages, several computational aspects turn out to be harder. It is therefore both of theoretical and of practical interest to investigate how far and in what ways Grammatical Inference algorithms developed for the string case are applicable to trees. This chapter surveys known results in this direction. We begin by recalling the basics of tree language theory. Then, the most popular learning scenarios and algorithms are presented. Several applications of Grammatical Inference of tree languages are reviewed in some detail. We conclude by suggesting a number of directions for future research.

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Treewidth, pathwidth and cospan decompositions with applications to graph-accepting tree automata

Cited by 11 publications

References 20 publications

Inverse Monoids of Higher-Dimensional Strings

Inverse Monoids of Higher-Dimensional Strings

Fuzzy graphs: algebraic structure and syntactic recognition

Learning Tree Languages

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