Skip to main content
SpringerLink
Log in

Acyclic Contextual Hyperedge Replacement: Decidability of Acyclicity and Generative Power

  • Conference paper
  • First Online:
Graph Transformation (ICGT 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13349))

Included in the following conference series:

Abstract

Graph grammars based on contextual hyperedge replacement (CHR) extend the generative power of the well-known hyperedge replacement (HR) grammars to an extent that makes them useful for practical modeling. Recent work has shown that acyclicity is a key condition for parsing CHR grammars efficiently. In this paper we show that acyclicity of CHR grammars is decidable and that the generative power of acyclic CHR grammars lies strictly between that of HR grammars and unrestricted CHR grammars.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Berglund, M.: Analyzing and pumping hyperedge replacement formalisms in a common framework. In: Echahed, R., Plump, D. (eds.) Pre-Proceedings Tenth International Workshop on Graph Computation Models, GCM@STAF 2019, Eindhoven, The Netherlands, 17 July 2019, pp. 17–32 (2019)

    Google Scholar 

  2. Drewes, F., Habel, A., Kreowski, H.J.: Hyperedge replacement graph grammars. In: Rozenberg, G. (ed.) Handbook of Graph Grammars and Computing by Graph Transformation. Vol. I: Foundations, chap. 2, pp. 95–162. World Scientific, Singapore (1997)

    Google Scholar 

  3. Drewes, F., Hoffmann, B.: Contextual hyperedge replacement. Acta Informatica 52(6), 497–524 (2015). https://doi.org/10.1007/s00236-015-0223-4

    Article  MathSciNet  MATH  Google Scholar 

  4. Drewes, F., Hoffmann, B., Minas, M.: Contextual hyperedge replacement. In: Schürr, A., Varró, D., Varró, G. (eds.) AGTIVE 2011. LNCS, vol. 7233, pp. 182–197. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-34176-2_16

    Chapter  Google Scholar 

  5. Drewes, F., Hoffmann, B., Minas, M.: Predictive top-down parsing for hyperedge replacement grammars. In: Parisi-Presicce, F., Westfechtel, B. (eds.) ICGT 2015. LNCS, vol. 9151, pp. 19–34. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21145-9_2

    Chapter  Google Scholar 

  6. Drewes, F., Hoffmann, B., Minas, M.: Predictive shift-reduce parsing for hyperedge replacement grammars. In: de Lara, J., Plump, D. (eds.) ICGT 2017. LNCS, vol. 10373, pp. 106–122. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-61470-0_7

    Chapter  Google Scholar 

  7. Drewes, F., Hoffmann, B., Minas, M.: Extending predictive shift-reduce parsing to contextual hyperedge replacement grammars. In: Guerra, E., Orejas, F. (eds.) ICGT 2019. LNCS, vol. 11629, pp. 55–72. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-23611-3_4

    Chapter  MATH  Google Scholar 

  8. Drewes, F., Hoffmann, B., Minas, M.: Formalization and correctness of predictive shift-reduce parsers for graph grammars based on hyperedge replacement. J. Log. Algebr. Methods Program. (JLAMP) 104, 303–341 (2019). https://doi.org/10.1016/j.jlamp.2018.12.006

    Article  MathSciNet  MATH  Google Scholar 

  9. Drewes, F., Hoffmann, B., Minas, M.: Rule-based top-down parsing for acyclic contextual hyperedge replacement grammars. In: Gadducci, F., Kehrer, T. (eds.) ICGT 2021. LNCS, vol. 12741, pp. 164–184. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-78946-6_9

    Chapter  Google Scholar 

  10. Ehrig, H., Ehrig, K., Prange, U., Taentzer, G.: Fundamentals of Algebraic Graph Transformation. EATCS Monographs, Springer, Heidelberg (2006). https://doi.org/10.1007/3-540-31188-2

    Book  MATH  Google Scholar 

  11. Habel, A.: Hyperedge Replacement: Grammars and Languages. LNCS, vol. 643. Springer, Heidelberg (1992). https://doi.org/10.1007/BFb0013875

    Book  MATH  Google Scholar 

  12. Habel, A., Kreowski, H., Vogler, W.: Metatheorems for decision problems on hyperedge replacement graph languages. Acta Informatica 26(7), 657–677 (1989). https://doi.org/10.1007/BF00288976

    Article  MathSciNet  MATH  Google Scholar 

  13. Jazayeri, M., Ogden, W.F., Rounds, W.C.: The intrinsically exponential complexity of the circularity problem for attribute grammars. Commun. ACM 18(12), 697–706 (1975). https://doi.org/10.1145/361227.361231

    Article  MathSciNet  MATH  Google Scholar 

  14. Knuth, D.E.: Semantics of context-free languages. Math. Sys. Theory 2(2), 127–145 (1968). https://doi.org/10.1007/BF01692511. Correction: [15]

  15. Knuth, D.E.: Semantics of context-free languages: correction. Math. Sys. Theory 5(2), 95–96 (1971). https://doi.org/10.1007/BF01702865

    Article  MathSciNet  MATH  Google Scholar 

  16. Navarro, M., Orejas, F., Pino, E., Lambers, L.: A navigational logic for reasoning about graph properties. J. Log. Algebraic Methods Program. 118, 100616 (2021). https://doi.org/10.1016/j.jlamp.2020.100616

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Umeå Universitet, Umeå, Sweden

    Frank Drewes

  2. Universität Bremen, Bremen, Germany

    Berthold Hoffmann

  3. Universität der Bundeswehr München, Neubiberg, Germany

    Mark Minas

Authors
  1. Frank Drewes
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Berthold Hoffmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mark Minas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Frank Drewes , Berthold Hoffmann or Mark Minas .

Editor information

Editors and Affiliations

  1. Université Paris Cité, Paris, France

    Nicolas Behr

  2. Computer Science and Engineering, Chalmers | Gothenburg University, Gothenburg, Sweden

    Daniel Strüber

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Drewes, F., Hoffmann, B., Minas, M. (2022). Acyclic Contextual Hyperedge Replacement: Decidability of Acyclicity and Generative Power. In: Behr, N., Strüber, D. (eds) Graph Transformation. ICGT 2022. Lecture Notes in Computer Science, vol 13349. Springer, Cham. https://doi.org/10.1007/978-3-031-09843-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-09843-7_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09842-0

  • Online ISBN: 978-3-031-09843-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation