Transformations Between Different Types of Unranked Bottom-Up Tree Automata

TL;DR

This paper investigates the complexity of transforming various forms of unranked bottom-up tree automata, providing bounds for state complexity in conversions between deterministic, nondeterministic, and other variants.

Contribution

It establishes upper and lower bounds for the state complexity involved in converting between different types of unranked tree automata, including various determinism and transition representations.

Findings

Derived bounds for automata state complexity conversions

Compared deterministic and nondeterministic automata variants

Analyzed impact of transition language representations

Abstract

We consider the representational state complexity of unranked tree automata. The bottom-up computation of an unranked tree automaton may be either deterministic or nondeterministic, and further variants arise depending on whether the horizontal string languages defining the transitions are represented by a DFA or an NFA. Also, we consider for unranked tree automata the alternative syntactic definition of determinism introduced by Cristau et al. (FCT'05, Lect. Notes Comput. Sci. 3623, pp. 68-79). We establish upper and lower bounds for the state complexity of conversions between different types of unranked tree automata.