Reducing Nondeterministic Tree Automata by Adding Transitions

TL;DR

This paper presents a saturation technique for nondeterministic tree automata that adds transitions to reduce automaton size efficiently, improving operations like merging, transition removal, and complementation.

Contribution

The authors introduce a novel saturation method that enhances automaton reduction algorithms, enabling more effective size reduction and faster computations in tree automata operations.

Findings

Saturation improves size reduction of automata.

Enhanced automata operations like complementation are faster.

Algorithm performs well on real and random automata.

Abstract

We introduce saturation of nondeterministic tree automata, a technique that consists of adding new transitions to an automaton while preserving its language. We implemented our algorithm on minotaut - a module of the tree automata library libvata that reduces the size of automata by merging states and removing superfluous transitions - and we show how saturation can make subsequent merge and transition-removal operations more effective. Thus we obtain a Ptime algorithm that reduces the size of tree automata even more than before. Additionally, we explore how minotaut alone can play an important role when performing hard operations like complementation, allowing to both obtain smaller complement automata and lower computation times. We then show how saturation can extend this contribution even further. We tested our algorithms on a large collection of automata from applications of libvata in shape analysis, and on different classes of randomly generated automata.