Reduction of Nondeterministic Tree Automata

TL;DR

This paper introduces an efficient algorithm for reducing nondeterministic tree automata size using novel transition pruning and state quotienting techniques, maintaining language while significantly shrinking automata.

Contribution

It presents a new reduction algorithm based on combined simulation and language inclusion criteria, with polynomial-time approximations for complex inclusion checks.

Findings

Produces substantially smaller automata than previous methods

Handles large automata efficiently in practical applications

Effective on automata from model checking and shape analysis

Abstract

We present an efficient algorithm to reduce the size of nondeterministic tree automata, while retaining their language. It is based on new transition pruning techniques, and quotienting of the state space w.r.t. suitable equivalences. It uses criteria based on combinations of downward and upward simulation preorder on trees, and the more general downward and upward language inclusions. Since tree-language inclusion is EXPTIME-complete, we describe methods to compute good approximations in polynomial time. We implemented our algorithm as a module of the well-known libvata tree automata library, and tested its performance on a given collection of tree automata from various applications of libvata in regular model checking and shape analysis, as well as on various classes of randomly generated tree automata. Our algorithm yields substantially smaller and sparser automata than all previously known reduction techniques, and it is still fast enough to handle large instances.