Two-pattern strings I: a recognition algorithm

Authors:
Frantisek Franek;Weilin Lu;W. F. Smyth
Affiliations:
Algorithms Research Group, Department of Computing & Software, McMaster University, Hamilton, ON, Canada L8S 4K1;Algorithms Research Group, Department of Computing & Software, McMaster University, Hamilton, ON, Canada L8S 4K1;Algorithms Research Group, Department of Computing & Software, McMaster University, Hamilton, ON, Canada L8S 4K1 and School of Computing, Curtin University, Perth WA 6845, Australia, and Departmen ...
Venue:
Journal of Discrete Algorithms
Year:
2003

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Two-pattern strings II-frequency of occurrence and substring complexity

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Abstract

This paper introduces a new class of strings on {a,b}, called two-pattern strings, that constitute a substantial generalization of Strumian strings while at the same time sharing many of their nice properties. In particular, we show in this paper that two-pattern strings can be recognized in time proportional to their length. This result is a prelude to showing that the repetitions in these substrings can also be computed in linear time, further that two-pattern strings occur in some sense frequently in the class of all strings on {a,b}.