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Patterns in Words versus Patterns in Trees: A Brief Survey and New Results

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1755))

Abstract

In this paper we study some natural problems related to specifying sets of words and trees by patterns.

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References

  1. D. Angluin. Finding patterns common to a set of strings. J. Comput. System Sci., 21:46–62, 1980.

    Article  MATH  MathSciNet  Google Scholar 

  2. D.R. Bean, A. Ehrenfeucht, and G.F. McNulty. Avoidable patterns in strings of symbols. Pacific J. Math., 85(2):261–294, 1979.

    MATH  MathSciNet  Google Scholar 

  3. J. Cassaigne. Motifs évitables et régularités dans les mots. Thèse de doctorat, Université Paris VI, 1994.

    Google Scholar 

  4. R. Cole, R. Hariharan, and P. Indyk. Tree pattern matching and subset matching in deterministic o(n log3 n)-time. In Proceedings of the 10th Annual ACM-SIAM Symposium on Discrete Algorithms, Baltymore, Maryland, January 17–19, 1999, pages 245–254. ACM, SIAM, 1999.

    Google Scholar 

  5. H. Comon and F. Jacquemard. Ground reducibility is EXPTIME-complete. In Proceedings, Twelth Annual IEEE Symposium on Logic in Computer Science, pages 26–34, Warsaw, Poland, 29 June–2 July 1997. IEEE Computer Society Press.

    Google Scholar 

  6. H. Comon. Unification et disunification. Théories et applications. Thèse de Doctorat d’Université, Institut Polytechnique de Grenoble (France), 1988.

    Google Scholar 

  7. M. Crochemore and W. Rytter. Squares, cubes, and time-space efficient string searching. Algorithmica, 13:405–425, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. Currie. Open problems in pattern avoidance. American Mathematical Monthly, 100:790–793, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  9. N. Dershowitz and J.-P. Jouannaud. Handbook of Theoretical Computer Science, volume B, chapter 6: Rewrite Systems, pages 244–320. Elsevier Science Publishers B. V. (North-Holland), 1990. Also as: Research report 478, LRI.

    Google Scholar 

  10. N. Dershowitz, J.-P. Jouannaud, and J.W. Klop. Open problems in rewriting. In R. V. Book, editor, Proceedings 4th Conference on Rewriting Techniques and Applications, Como (Italy), volume 488 of Lecture Notes in Computer Science, pages 445–456. Springer-Verlag, 1991.

    Google Scholar 

  11. G. Filè. The relation of two patterns with comparable languages. In R. Cori M. Wirsing, editor, Proceedings of the 5th Annual Symposium on Theoretical Aspects of Computer Science (STACS’ 88), volume 294 of Lecture Notes in Computer Science, pages 184–192, Bordeaux, France, February 1988. Springer.

    Google Scholar 

  12. M. Garey and D. Johnson. Computers and Intractability. A guide to the theory of NP-completeness. W. Freeman and Compagny, New York, 1979.

    MATH  Google Scholar 

  13. G. Gottlob and R. Pichler. Working with ARMs: Complexity results on atomic representations of Herbrand models. In Proceedings of LICS’99, 1999. to appear, available from http://www.dbai.tuwien.ac.at/staff/gottlob/arms.ps.

  14. F. Gécseg and M. Steinby. Tree automata. Akadémiai Kiadó, Budapest, Hungary, 1984.

    MATH  Google Scholar 

  15. D. Hofbauer and M. Huber. Computing linearizations using test sets. In M. Rusinowitch and J.-L. Rémy, editors, Proceedings 3rd International Workshop on Conditional Term Rewriting Systems, Pont-à-Mousson (France), pages 145–149. CRIN and INRIA-Lorraine, 1992.

    Google Scholar 

  16. C. M. Hoffmann and M. J. O’Donnell. Pattern matching in trees. Journal of the ACM, 29(1):68–95, 1982.

    Article  MATH  MathSciNet  Google Scholar 

  17. J. E. Hopcroft and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley Publishing Company, Reading, Mass., USA, 1979.

    MATH  Google Scholar 

  18. J.-P. Jouannaud and E. Kounalis. Automatic proofs by induction in theories without constructors. Information and Computation, 82:1–33, 1989.

    Article  MATH  MathSciNet  Google Scholar 

  19. T. Jiang, A. Salomaa, K. Salomaa, and S. Yu. Inclusion is undecidable for pattern languages. In Svante Carlsson Andrzej Lingas, Rolf G. Karlsson, editor, Automata, Languages and Programming, 20th International Colloquium, volume 700 of Lecture Notes in Computer Science, pages 301–312, Lund, Sweden, 5–9 July 1993. Springer-Verlag.

    Google Scholar 

  20. L. Kari, A. Mateescu, G. Paun, and A. Salomaa. Multi-pattern languages. Theoretical Computer Science, 141:253–268, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  21. D. Kapur, P. Narendran, D. J. Rosenkrantz, and H. Zhang. Sufficient completeness, ground-reducibility and their complexity. Acta Informatica, 28:311–350, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  22. D. Kapur, P. Narendran, and H. Zhang. On sufficient completeness and related properties of term rewriting systems. Acta Informatica, 24:395–415, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  23. G. Kucherov and D. Plaisted. The complexity of some complementation problems. submitted, 1998.

    Google Scholar 

  24. G. Kucherov and M. Rusinowitch. Complexity of testing ground reducibility for linear word rewriting systems with variables. In Proceedings 4th International Workshop on Conditional and Typed Term Rewriting Systems, Jerusalem (Israel), volume 968 of Lecture Notes in Computer Science, pages 262–275. Springer-Verlag, 1995.

    Google Scholar 

  25. G. Kucherov and M. Rusinowitch. Undecidability of ground reducibility for word rewriting systems with variables. Information Processing Letters, 53:209–215, 1995.

    Article  MATH  MathSciNet  Google Scholar 

  26. G. Kucherov and M. Tajine. Decidability of regularity and related properties of ground normal form languages. In M. Rusinowitch and J.-L. Rémy, editors, Proceedings 3rd International Workshop on Conditional Term Rewriting Systems, Pont-à-Mousson (France), pages 150–156. CRIN and INRIA-Lorraine, 1992.

    Google Scholar 

  27. G. Kucherov and M. Tajine. Decidability of regularity and related properties of ground normal form languages. Information and Computation, 118(1):91–100, April 1995.

    Article  MATH  MathSciNet  Google Scholar 

  28. G. A. Kucherov. On relationship between term rewriting systems and regular tree languages. In R. V. Book, editor, Proceedings 4th Conference on Rewriting Techniques and Applications, Como (Italy), volume 488 of Lecture Notes in Computer Science, pages 299–311. Springer-Verlag, April 1991.

    Google Scholar 

  29. J.-L. Lassez and K. Marriot. Explicit representation of terms defined by counter examples. Journal of Automated Reasoning, 3(3):301–318, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  30. A. Mateescu and A. Salomaa. Nondeterminism in patterns. In P. Enjalbert, E.W. Mayr, and K.W. Wagner, editors, Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science (STACS’94), Caen, France, February 1994, volume 775 of Lecture Notes in Computer Science, pages 661–668. Springer-Verlag, 1994.

    Google Scholar 

  31. J. Néraud. Detecting morphic images of a word: On the rank of a pattern. Acta Informatica, 32:477–489, 1995.

    MATH  MathSciNet  Google Scholar 

  32. M. Nivat and A. Podelski, editors. Tree Automata and Languages. Studies in Computer Science and Artificial Intelligence 10. North-Holland, 1992.

    Google Scholar 

  33. R. Pichler. The explicit representability of implicit generalizations. submitted, april 1999.

    Google Scholar 

  34. D. Plaisted. Semantic confluence and completion method. Information and Control, 65:182–215, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  35. R. Ramesh and I.V. Ramakrishnan. Nonlinear pattern matching in trees. Journal of the ACM, 39(2):295–316, April 1992.

    Article  MATH  MathSciNet  Google Scholar 

  36. T. Shinohara. Polynomial time inference of pattern langages and its applications. In Proceedings of the 7th IBM Symposium on Mathematical Foundations of Computer Science, Mathematical Theory of Computations/The Complexity of Algorithms, pages 191–209, 1982.

    Google Scholar 

  37. S. Vágvölgyi and R. Gilleron. For a rewriting system it is decidable whether the set of irreducible ground terms is recognizable. Bulletin of European Association for Theoretical Computer Science, 48:197–209, 1992.

    MATH  Google Scholar 

  38. A.I. Zimin. Blocking sets of terms. Math. USSR Sbornik, 47:353–364, 1984. Original version in russian published in 1982, 119 (3), 363–375.

    Article  MATH  Google Scholar 

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Kucherov, G., Rusinowitch, M. (2000). Patterns in Words versus Patterns in Trees: A Brief Survey and New Results. In: Bjøner, D., Broy, M., Zamulin, A.V. (eds) Perspectives of System Informatics. PSI 1999. Lecture Notes in Computer Science, vol 1755. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46562-6_25

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  • DOI: https://doi.org/10.1007/3-540-46562-6_25

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