Context-Free Trees

TL;DR

This paper studies context-free trees, showing they can be described by finite-state automata and analyzing the computational complexity of their isomorphism problem.

Contribution

It introduces a finite-state description for context-free trees and establishes the NL-completeness of the isomorphism problem for deterministic cases.

Findings

Context-free trees can be encoded with multi-edge NFAs.

Deterministic context-free trees have a rooted and non-rooted isomorphism problem that is NL-complete.

Abstract

Muller and Schupp introduced the concept of context-free graphs (originating from Cayley graphs of context-free groups). These graphs are always tree-like (i.e. quasi-isometric to a tree) and in this paper we investigate the subclass of bona fide context-free trees. We show that they have a finite-state description using multi-edge NFAs and that this specializes to certain partial DFAs in the case of deterministic graphs. We investigate this form of encoding algorithmically and show that the isomorphism problem for deterministic context-free trees is NL-complete in the rooted and the non-rooted case.