Minimal Ascending and Descending Tree Automata

  • Authors:
  • Maurice Nivant;Andreas Podelski

  • Affiliations:
  • -;-

  • Venue:
  • SIAM Journal on Computing
  • Year:
  • 1997

Quantified Score

Hi-index 0.00

Visualization

Abstract

We propose a generalization of the notion "deterministic" to "l-r-deterministic" for descending tree automata (also called root-to-frontier). The corresponding subclass of recognizable tree languages is characterized by a structural property that we name "homogeneous." Given a descending tree automaton recognizing a homogeneous tree language, it can be left-to-right (l-r) determinized and then minimized. The obtained minimal l-r-deterministic tree automaton is characterized algebraically. We exhibit a formal correspondence between the two evaluation modes on trees (ascending and descending) and the two on words (right-to-left and left-to-right). This is possible by embedding trees into the free monoid of pointed trees. We obtain a unified view of the theories of minimization of deterministic ascending and l-r-deterministic descending tree automata.