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Computing with graph relabelling systems with priorities

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 532))

Abstract

In this paper, the computational power of the noetherian Graph Relabelling systems with Priorities (PGRS for short) is studied. The PGRS's are considered as recognizers for sets of graphs and for sets of 1-sourced graphs. We show that the PGRS's are strictly more powerful for the 1-sourced graphs than for the graphs. Furthermore every set of 1-sourced graphs definable in First Order Logic is recognizable by some PGRS.

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References

  1. M. Billaud, Some Backtracking Graphs Algorithms expressed by Graph Rewriting Systems with Priorities, Rapport Interne no 8989, LaBRI, Univ. Bordeaux I.

    Google Scholar 

  2. M. Billaud, Un interpréteur pour les Systèmes de Réécriture de Graphes avec Priorités, Rapport Interne no 9040, LaBRI, Univ. Bordeaux I.

    Google Scholar 

  3. M. Billaud, P. Lafon, Y. Métivier and E. Sopena, Graph Rewriting Systems with Priorities: Definitions and Applications, Rapport Interne no 8909, LaBRI, Univ. Bordeaux I.

    Google Scholar 

  4. M. Billaud, P. Lafon, Y. Métivier and E. Sopena, Graph Rewriting Systems with Priorities, in Graph-Theoretic Concepts in Computer Science, 15th Workshop on Graphs'89, LNCS no 411, pp. 94–106.

    Google Scholar 

  5. B. Courcelle, Some applications of logic of universal algebra, and of category theory to the theory of graph transformations, Bulletin of E.A.T.C.S. no 36 (1988), pp. 161–218.

    Google Scholar 

  6. B. Courcelle, The monadic second-order logic of graphs V: on closing the gap between definability and recognizability, Rapport Interne no 8991, LaBRI, Univ. Bordeaux I.

    Google Scholar 

  7. B. Courcelle, The monadic second-order logic of graphs VI: on several representations of graphs by relational stuctures. Rapport Interne no 8999, LaBRI, Univ. Bordeaux I.

    Google Scholar 

  8. B. Courcelle, The monadic second-order logic of graphs I. Recognizable sets of finite graphs, Information and Computation vol. 85 no 1 (1990), pp. 12–75.

    Article  Google Scholar 

  9. J. Doner, Tree Acceptors and Some of Their Applications, Journal of Computer and System Sciences 4 (1970), pp. 406–451.

    Google Scholar 

  10. J. Fris, Grammars with partial ordering of the rules, Information Control 12 (1968), pp. 415–425.

    Article  Google Scholar 

  11. H. Gaifman, On local and non-local properties, Proc. of the Herbrand Symposium, Logic Colloquim'81, J. Stern ed., North-Holland Pub. Co. (1982), pp. 105–135.

    Google Scholar 

  12. F. Gécseg and M. Steinby, Tree automata, Akadémiai Kiado-Budapest (1984).

    Google Scholar 

  13. J.E. Hopcroft and J.D. Ullman, Some Results on Tape-Bounded Turing Machines, Journal of the Association for Computing Machinery, Vol. 16, no 1 (1967), pp. 168–177.

    Google Scholar 

  14. J.E. Hopcroft and J.D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley (1979).

    Google Scholar 

  15. N. Immerman, Languages that capture complexity classes, SIAM J. Comput., vol. no 4 (1987), pp. 760–778.

    Google Scholar 

  16. I. Litovsky and Y. Métivier, Computing with Graphs Rewriting Systems with Priorities, Rapport Interne du LaBRI, Univ. Bordeaux I.

    Google Scholar 

  17. A.A. Markov, Theory of Algorithms, Jerusalem: Israel Program for Scientific Translations (1961).

    Google Scholar 

  18. A. Salomaa, Formal Languages, Academic Press (1979).

    Google Scholar 

  19. W. Tutte, Graph Theory, Addison Wesley (1984).

    Google Scholar 

  20. A. Yasuhara, Recursive function theory & logic, Academic Press (1971).

    Google Scholar 

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Hartmut Ehrig Hans-Jörg Kreowski Grzegorz Rozenberg

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© 1991 Springer-Verlag Berlin Heidelberg

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Litovsky, I., Métivier, Y. (1991). Computing with graph relabelling systems with priorities. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017412

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  • DOI: https://doi.org/10.1007/BFb0017412

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54478-4

  • Online ISBN: 978-3-540-38395-6

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