Operational State Complexity of Deterministic Unranked Tree Automata

TL;DR

This paper analyzes the state complexity of fundamental operations on deterministic unranked tree automata, providing tight bounds for union, intersection, and a novel bound for tree concatenation, highlighting differences from string automata.

Contribution

It establishes tight bounds for union, intersection, and introduces a new upper bound for tree concatenation in deterministic unranked tree automata.

Findings

Bounds for union and intersection are established.

A tight upper bound for tree concatenation is derived.

Tree concatenation complexity differs from string automata.

Abstract

We consider the state complexity of basic operations on tree languages recognized by deterministic unranked tree automata. For the operations of union and intersection the upper and lower bounds of both weakly and strongly deterministic tree automata are obtained. For tree concatenation we establish a tight upper bound that is of a different order than the known state complexity of concatenation of regular string languages. We show that (n+1) ( (m+1)2^n-2^(n-1) )-1 vertical states are sufficient, and necessary in the worst case, to recognize the concatenation of tree languages recognized by (strongly or weakly) deterministic automata with, respectively, m and n vertical states.