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On Matching Generalised Repetitive Patterns

  • Joel D. Day
  • Pamela Fleischmann
  • Florin Manea
  • Dirk Nowotka
  • Markus L. Schmid
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11088)

Abstract

A pattern is a string with terminals and variables (which can be uniformly replaced by terminal words). Given a class \(\mathcal {C}\) of patterns (with variables), we say a pattern \(\alpha \) is a \(\mathcal {C}\)-(pseudo-)repetition if its skeleton – the result of removing all terminal symbols to leave only the variables – is a (pseudo-)repetition of a pattern from \(\mathcal {C}\). We introduce a large class of patterns which generalises several known classes such as the k-local and bounded scope coincidence degree patterns, and show that for this class, \( \mathcal {C}\)-(pseudo-)repetitions can be matched in polynomial time. We also show that for most classes \(\mathcal {C}\), the class of \(\mathcal {C}\)-(pseudo-)repetitions does not have bounded treewidth. Finally, we show that if the notion of repetition is relaxed, so that in each occurrence the variables may occur in a different order, the matching problem is NP-complete, even in severely restricted cases.

Keywords

Pattern matching with variables Repetitions 

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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Joel D. Day
    • 1
  • Pamela Fleischmann
    • 1
  • Florin Manea
    • 1
  • Dirk Nowotka
    • 1
  • Markus L. Schmid
    • 2
  1. 1.Kiel UniversityKielGermany
  2. 2.Trier UniversityTrierGermany

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