Five facets of hyperedge replacement beyond context-freeness

Kreowski, Hans‐Jörg

doi:10.1007/3-540-57163-9_5

Cited by 4 publications

(1 citation statement)

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“…We call our new class the parallel hyperedge replacement string (PHRS) languages, and show that the class strictly contains both the classes of MCF and ET0L languages, that it is a substitution and iterated substitution closed full abstract family of languages, and that PHRS group languages are closed under free product. While parallel hyperedge replacement has been considered before, most notably by Habel and Kreowski (separately) [13,18,19], the work is not extensive and does not consider repetition-freeness, rational control, or string generational power. Our long term goal is to place the word problem for as many hyperbolic groups as possible in the PHRS class.…”

Section: Introductionmentioning

confidence: 99%

Parallel Hyperedge Replacement String Languages

Campbell

2021

Electron. Proc. Theor. Comput. Sci.

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There are many open questions surrounding the characterisation of groups with context-sensitive word problem. Only in 2018 was it shown that all finitely generated virtually Abelian groups have multiple context-free word problems, and it is a long-standing open question as to where to place the word problems of hyperbolic groups in the formal language hierarchy. In this paper, we introduce a new language class called the parallel hyperedge replacement string languages, show that it contains all multiple context-free and ET0L languages, and lay down the foundations for future work that may be able to place the word problems of many hyperbolic groups in this class.

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Section: Introductionmentioning

confidence: 99%

Parallel Hyperedge Replacement String Languages

Campbell

2021

Electron. Proc. Theor. Comput. Sci.

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On the interleaving semantics of transformation units — A step into GRACE

Kreowski

Kuske

1996

Lecture Notes in Computer Science

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Graph Transformation Units with Interleaving Semantics

Kreowski

Kuske

1999

Form. Asp. Comput.

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Abstract. The aim of the paper is to introduce the notion of a transformation unit together with its interleaving semantics and to study it as a means of constructing large graph transformation systems from small ones in a structured and systematic way. A transformation unit comprises a set of rules, descriptions of initial and terminal graphs, and a control condition. Moreover, it may import other transformation units for structuring purposes. Its semantics is a binary relation between initial and terminal graphs which is given by interleaving sequences. As a generalization of ordinary derivations, an interleaving sequence consists of direct derivation steps interleaved with calls of imported transformation units. It must obey the control condition and may be seen as a kind of structured derivation. The introduced framework is independent of a particular graph transformation approach and, therefore, it may enhance the usefulness of graph transformations in many contexts.

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Five facets of hyperedge replacement beyond context-freeness

Cited by 4 publications

References 18 publications

Parallel Hyperedge Replacement String Languages

Parallel Hyperedge Replacement String Languages

On the interleaving semantics of transformation units — A step into GRACE

Graph Transformation Units with Interleaving Semantics

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