Abstract
In the context of this paper, a pattern is a string that contains variables and terminals. A pattern α matches a terminal word w if w can be obtained by uniformly substituting the variables of α by terminal words. It is a well-known fact that deciding whether a given terminal word matches a given pattern is an NP-complete problem. In this work, we consider numerous parameters of this problem and for all possible combinations of these parameters, we investigate the question whether or not the variant obtained by bounding these parameters by constants can be solved efficiently.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Amir, A., Aumann, Y., Cole, R., Lewenstein, M., Porat, E.: Function matching: Algorithms, applications, and a lower bound. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 929–942. Springer, Heidelberg (2003)
Amir, A., Nor, I.: Generalized function matching. Journal of Discrete Algorithms 5, 514–523 (2007)
Angluin, D.: Finding patterns common to a set of strings. In: Proc. 11th Annual ACM Symposium on Theory of Computing, STOC 1979, pp. 130–141 (1979)
Angluin, D.: Finding patterns common to a set of strings. Journal of Computer and System Sciences 21, 46–62 (1980)
Baker, B.S.: Parameterized pattern matching: Algorithms and applications. Journal of Computer and System Sciences 52, 28–42 (1996)
Bremer, J., Freydenberger, D.D.: Inclusion problems for patterns with a bounded number of variables. In: Gao, Y., Lu, H., Seki, S., Yu, S. (eds.) DLT 2010. LNCS, vol. 6224, pp. 100–111. Springer, Heidelberg (2010)
Câmpeanu, C., Salomaa, K., Yu, S.: A formal study of practical regular expressions. International Journal of Foundations of Computer Science 14, 1007–1018 (2003)
Clifford, R., Harrow, A.W., Popa, A., Sach, B.: Generalised matching. In: Karlgren, J., Tarhio, J., Hyyrö, H. (eds.) SPIRE 2009. LNCS, vol. 5721, pp. 295–301. Springer, Heidelberg (2009)
Ehrenfeucht, A., Rozenberg, G.: Finding a homomorphism between two words is NP-complete. Information Processing Letters 9, 86–88 (1979)
Freydenberger, D.D., Reidenbach, D.: Bad news on decision problems for patterns. Information and Computation 208, 83–96 (2010)
Freydenberger, D.D., Reidenbach, D., Schneider, J.C.: Unambiguous morphic images of strings. International Journal of Foundations of Computer Science 17, 601–628 (2006)
Friedl, J.E.F.: Mastering Regular Expressions, 3rd edn. O’Reilly, Sebastopol (2006)
Geilke, M., Zilles, S.: Learning relational patterns. In: Kivinen, J., Szepesvári, C., Ukkonen, E., Zeugmann, T. (eds.) ALT 2011. LNCS, vol. 6925, pp. 84–98. Springer, Heidelberg (2011)
Harju, T., Karhumäki, J.: Morphisms. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, ch. 7, pp. 439–510. Springer (1997)
Ibarra, O., Pong, T.-C., Sohn, S.: A note on parsing pattern languages. Pattern Recognition Letters 16, 179–182 (1995)
Jiang, T., Kinber, E., Salomaa, A., Salomaa, K., Yu, S.: Pattern languages with and without erasing. International Journal of Computer Mathematics 50, 147–163 (1994)
Jiang, T., Salomaa, A., Salomaa, K., Yu, S.: Decision problems for patterns. Journal of Computer and System Sciences 50, 53–63 (1995)
Kratochvíl, J., Křivánek, M.: On the computational complexity of codes in graphs. In: Koubek, V., Janiga, L., Chytil, M.P. (eds.) MFCS 1988. LNCS, vol. 324, pp. 396–404. Springer, Heidelberg (1988)
Mateescu, A., Salomaa, A.: Finite degrees of ambiguity in pattern languages. RAIRO Informatique Théoretique et Applications 28, 233–253 (1994)
Ng, Y.K., Shinohara, T.: Developments from enquiries into the learnability of the pattern languages from positive data. Theoretical Computer Science 397, 150–165 (2008)
Ohlebusch, E., Ukkonen, E.: On the equivalence problem for E-pattern languages. Theoretical Computer Science 186, 231–248 (1997)
Reidenbach, D.: A non-learnable class of E-pattern languages. Theoretical Computer Science 350, 91–102 (2006)
Reidenbach, D.: Discontinuities in pattern inference. Theoretical Computer Science 397, 166–193 (2008)
Reidenbach, D., Schmid, M.L.: A polynomial time match test for large classes of extended regular expressions. In: Domaratzki, M., Salomaa, K. (eds.) CIAA 2010. LNCS, vol. 6482, pp. 241–250. Springer, Heidelberg (2011)
Reidenbach, D., Schmid, M.L.: Patterns with bounded treewidth. In: Dediu, A.-H., Martín-Vide, C. (eds.) LATA 2012. LNCS, vol. 7183, pp. 468–479. Springer, Heidelberg (2012)
Schmid, M.L.: A note on the complexity of matching patterns with variables. Information Processing Letters (Submitted)
Schmid, M.L.: On the Membership Problem for Pattern Languages and Related Topics. PhD thesis, Department of Computer Science, Loughborough University (2012)
Shinohara, T.: Polynomial time inference of extended regular pattern languages. In: Goto, E., Furukawa, K., Nakajima, R., Nakata, I., Yonezawa, A. (eds.) RIMS 1982. LNCS, vol. 147, pp. 115–127. Springer, Heidelberg (1983)
Shinohara, T.: Polynomial time inference of pattern languages and its application. In: Proc. 7th IBM Symposium on Mathematical Foundations of Computer Science, pp. 191–209 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fernau, H., Schmid, M.L. (2013). Pattern Matching with Variables: A Multivariate Complexity Analysis. In: Fischer, J., Sanders, P. (eds) Combinatorial Pattern Matching. CPM 2013. Lecture Notes in Computer Science, vol 7922. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38905-4_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-38905-4_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-38904-7
Online ISBN: 978-3-642-38905-4
eBook Packages: Computer ScienceComputer Science (R0)