Global One-Counter Tree Automata

TL;DR

This paper introduces global one-counter tree automata (GOCTA), a new model that processes trees with a single counter passed lexicographically, revealing unique computational properties and decidability results.

Contribution

The paper defines GOCTA, compares their expressive power with traditional counter tree automata, and analyzes their decidability and complexity properties.

Findings

GOCTA and counter tree automata recognize incomparable language classes.

Emptiness problem for GOCTA is undecidable.

Membership problem for GOCTA is in P.

Abstract

We introduce global one-counter tree automata (GOCTA) which deviate from usual counter tree automata by working on only one counter which is passed through the tree in lexicographical order, rather than duplicating the counter at every branching position. We compare the capabilities of GOCTA to those of counter tree automata and obtain that their classes of recognizable tree languages are incomparable. Moreover, we show that the emptiness problem of GOCTA is undecidable while, in stark contrast, their membership problem is in P.