Optimised determinisation and completion of finite tree automata

TL;DR

This paper introduces a new algorithm for determinising and completing finite tree automata that maintains worst-case complexity but significantly improves practical performance through a compact product form transition representation.

Contribution

The paper presents a novel determinisation and completion algorithm for finite tree automata using a compact product form, enhancing efficiency without increasing theoretical complexity.

Findings

Algorithm performs better than existing methods in practice

Transitions are generated in a compact product form

Experimental evaluation shows improved efficiency on large automata

Abstract

Determinisation and completion of finite tree automata are important operations with applications in program analysis and verification. However, the complexity of the classical procedures for determinisation and completion is high. They are not practical procedures for manipulating tree automata beyond very small ones. In this paper we develop an algorithm for determinisation and completion of finite tree automata, whose worst-case complexity remains unchanged, but which performs far better than existing algorithms in practice. The critical aspect of the algorithm is that the transitions of the determinised (and possibly completed) automaton are generated in a potentially very compact form called product form, which can reduce the size of the representation dramatically. Furthermore, the representation can often be used directly when manipulating the determinised automaton. The paper contains an experimental evaluation of the algorithm on a large set of tree automata examples.