State complexity of kleene-star operations on trees

  • Authors:

  • Xiaoxue Piao;Kai Salomaa

  • Affiliations:

  • School of Computing, Queen's University, Kingston, Ontario, Canada;School of Computing, Queen's University, Kingston, Ontario, Canada

  • Venue:
  • WTCS'12 Proceedings of the 2012 international conference on Theoretical Computer Science: computation, physics and beyond
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

The concatenation of trees can be defined either as a sequential or a parallel operation, and the corresponding iterated operation gives an extension of Kleene-star to tree languages. Since the sequential tree concatenation is not associative, we get two essentially different iterated sequential concatenation operations that we call the bottom-up star and top-down star operation, respectively. We establish that the worst-case state complexity of bottom-up star is $(n + \frac{3}{2}) \cdot 2^{n-1}$ . The bound differs by an order of magnitude from the corresponding result for string languages. The state complexity of top-down star is similar as in the string case. The iteration of the parallel concatenation has to be defined slightly differently in order to yield a regularity preserving operation.