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Unfolding Grammars in Adhesive Categories

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Algebra and Coalgebra in Computer Science (CALCO 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5728))

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Abstract

We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories. The unfolding construction is characterized as a coreflection, i.e. the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of grammars.

As the unfolding represents potentially infinite computations, we need to work in adhesive categories with “well-behaved” colimits of ω-chains of mono-morphisms. Compared to previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism.

Supported by DFG project SANDS and project AVIAMO of the University of Padova.

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References

  1. Baldan, P.: Modelling Concurrent Computations: from Contextual Petri Nets to Graph Grammars. PhD thesis, Dipartimento di Informatica, Università di Pisa (2000)

    Google Scholar 

  2. Baldan, P., Corradini, A., Heindel, T., König, B., Sobociński, P.: Processes for adhesive rewriting systems. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006. LNCS, vol. 3921, pp. 202–216. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  3. Baldan, P., Corradini, A., König, B.: A framework for the verification of infinite-state graph transformation systems. Information and Computation 206, 869–907 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Baldan, P., Corradini, A., Montanari, U., Ribeiro, L.: Unfolding Semantics of Graph Transformation. Information and Computation 205, 733–782 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  5. Baldan, P., Chatain, T., Haar, S., König, B.: Unfolding-based diagnosis of systems with an evolving topology. In: van Breugel, F., Chechik, M. (eds.) CONCUR 2008. LNCS, vol. 5201, pp. 203–217. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Benveniste, A., Fabre, E., Haar, S., Jard, C.: Diagnosis of asynchronous discrete event systems, a net unfolding approach. IEEE Transactions on Automatic Control 48(5), 714–727 (2003)

    Article  MathSciNet  Google Scholar 

  7. Birkhoff, G.: Lattice Theory. American Mathematical Society (1967)

    Google Scholar 

  8. Cockett, R., Guo, X.: Join restriction categories and the importance of being adhesive. Unpublished manuscript, slides from CT 2007 (2007), http://pages.cpsc.ucalgary.ca/~robin/talks/jrCat.pdf

  9. Ehrig, H., Habel, A., Kreowski, H.-J., Parisi-Presicce, F.: Parallelism and Concurrency in High-Level Replacement Systems. Mathematical Structures in Computer Science 1, 361–404 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  10. Ehrig, H., Pfender, M., Schneider, H.J.: Graph-grammars: an algebraic approach. In: Proc. of IEEE Conf. on Automata and Switching Theory, pp. 167–180 (1973)

    Google Scholar 

  11. Hayman, J., Winskel, G.: The unfolding of general Petri nets. In: Proc. of FSTTCS 2008. Dagstuhl Seminar Proceedings, vol. (08004) (2008)

    Google Scholar 

  12. Heindel, T., Sobociński, P.: Van Kampen colimits as bicolimits in Span. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds.) CALCO 2009. LNCS, vol. 5728, pp. 335–349. Springer, Heidelberg (2009)

    Google Scholar 

  13. Johnstone, P.T.: Sketches of an Elephant, vol. 1. Oxford Science Publications (2002)

    Google Scholar 

  14. Lack, S., Sobociński, P.: Adhesive and quasiadhesive categories. Theoretical Informatics and Applications 39(2), 511–546 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  15. Lack, S., Sobociński, P.: Toposes are adhesive. In: Corradini, A., Ehrig, H., Montanari, U., Ribeiro, L., Rozenberg, G. (eds.) ICGT 2006. LNCS, vol. 4178, pp. 184–198. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Löwe, M.: Algebraic approach to single-pushout graph transformation. Theoretical Computer Science 109, 181–224 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  17. McMillan, K.L.: Symbolic Model Checking. Kluwer Academic Publishers, Dordrecht (1993)

    Book  MATH  Google Scholar 

  18. Meseguer, J., Montanari, U., Sassone, V.: On the semantics of Place/Transition Petri nets. Mathematical Structures in Computer Science 7(4), 359–397 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  19. Robinson, E., Rosolini, G.: Categories of partial maps. Inf. Comput. 79(2), 95–130 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  20. Winskel, G.: Event structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Matematica Pura e Applicata, Università di Padova, Italy

    Paolo Baldan

  2. Dipartimento di Informatica, Università di Pisa, Italy

    Andrea Corradini

  3. Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Germany

    Tobias Heindel & Barbara König

  4. ECS, University of Southampton, United Kingdom

    Paweł Sobociński

Authors
  1. Paolo Baldan
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  2. Andrea Corradini
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  3. Tobias Heindel
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  4. Barbara König
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  5. Paweł Sobociński
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Leicester, University Road, LE1 7RH, Leicester, UK

    Alexander Kurz

  2. Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze, 206, 33100, Udine, Italy

    Marina Lenisa

  3. Faculty of Mathematics, Informatics and Mechanics, Warsaw University, ul. Banacha 2, 02-097, Warsaw, Poland

    Andrzej Tarlecki

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Baldan, P., Corradini, A., Heindel, T., König, B., Sobociński, P. (2009). Unfolding Grammars in Adhesive Categories. In: Kurz, A., Lenisa, M., Tarlecki, A. (eds) Algebra and Coalgebra in Computer Science. CALCO 2009. Lecture Notes in Computer Science, vol 5728. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03741-2_24

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  • DOI: https://doi.org/10.1007/978-3-642-03741-2_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03740-5

  • Online ISBN: 978-3-642-03741-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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