Complexity of Makanin's Algorithm

@article{Koscielski1996ComplexityOM,
  title={Complexity of Makanin's Algorithm},
  author={Antoni Koscielski and Leszek Pacholski},
  journal={J. ACM},
  year={1996},
  volume={43},
  pages={670-684}
}
The exponent of periodicity is an important factor in estimates of complexity of word-unification algorithms. We prove that the exponent of periodicity of a minimal solution of a word equation is of order 2<supscrpt>1.07d</supscrpt>, where <italic>d</italic> is the length of the equation. We also give a lower bound 2<supscrpt>0.29d</supscrpt> so our upper bound is almost optimal and exponentially better than the original bound <italic>(6d)<supscrpt>22d4</supscrpt>+ 2</italic>. Consequently, our… CONTINUE READING

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