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Real-time recognition of substring repetition and reversal

Abstract

Real-time multitape Turing machine algorithms are presented for recognizing the languages {wxyxz∈Σ*:|w|=r|x,|z| =t|x|} and {wxyx R z ∈Σ*:|w|=r|x,|z| =t|x|} for fixedr, s, andt and for string-matching with “forced mismatches.”

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Additional information

This research was supported in part by the National Science Foundation under Grant MCS77-06613 (first author) and the Bat-Sheva Fund (second author). Part of the work was conducted while the second author was at the IBM Thomas J. Watson Research Center, Yorktown Heights, New York. A preliminary report was included in a paper the authors presented at the Seventeenth Annual IEEE Symposium on Foundations of Computer Science, Houston, Texas, October 1976.

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Seiferas, J., Galil, Z. Real-time recognition of substring repetition and reversal. Math. Systems Theory 11, 111–146 (1977). https://doi.org/10.1007/BF01768472

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Key words and phrases

  • palindrome
  • real-time
  • Turing machine
  • language recognition
  • repetition
  • reversal
  • string-matching
  • pattern-matching
  • periodicity
  • predictability condition