Pattern Discovery in Colored Strings

Authors Zsuzsanna Lipták , Simon J. Puglisi , Massimiliano Rossi

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Author Details

Zsuzsanna Lipták
  • Department of Computer Science, University of Verona, Italy
Simon J. Puglisi
  • Department of Computer Science, University of Helsinki, Finland
Massimiliano Rossi
  • Department of Computer and Information Science and Engineering, University of Florida, Gainesville, FL, USA


We thank Johannes Fischer, Travis Gagie, and Ferdinando Cicalese for interesting discussions, and Alessandro Danese for providing an updated data set of traces.

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Zsuzsanna Lipták, Simon J. Puglisi, and Massimiliano Rossi. Pattern Discovery in Colored Strings. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


We consider the problem of identifying patterns of interest in colored strings. A colored string is a string in which each position is colored with one of a finite set of colors. Our task is to find substrings that always occur followed by the same color at the same distance. The problem is motivated by applications in embedded systems verification, in particular, assertion mining. The goal there is to automatically infer properties of the embedded system from the analysis of its simulation traces. We show that the number of interesting patterns is upper-bounded by 𝒪(n²) where n is the length of the string. We introduce a baseline algorithm with 𝒪(n²) running time which identifies all interesting patterns for all colors in the string satisfying certain minimality conditions. When one is interested in patterns related to only one color, we provide an algorithm that identifies patterns in 𝒪(n²log n) time, but is faster than the first algorithm in practice, both on simulated and on real-world patterns.

Subject Classification

ACM Subject Classification
  • Theory of computation → Design and analysis of algorithms
  • property testing
  • suffix tree
  • pattern mining


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