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When Simulation Meets Antichains (on Checking Language Inclusion of NFAs)

Summary: When Simulation Meets Antichains
(on Checking Language Inclusion of NFAs)
Parosh Aziz Abdulla1, Yu-Fang Chen1, Lukás Holík2, Richard Mayr3, and Tomás Vojnar2
1Uppsala University 2Brno University of Technology 3University of Edinburgh
Abstract. We describe a new and more efficient algorithm for checking univer-
sality and language inclusion on nondeterministic finite word automata (NFA)
and tree automata (TA). To the best of our knowledge, the antichain-based ap-
proach proposed by Wulf et al. was the most efficient one so far. Our idea is
to exploit a simulation relation on the states of finite automata to accelerate the
antichain-based algorithms. Normally, a simulation relation can be obtained fairly
efficiently, and it can help the antichain-based approach to prune out a large por-
tion of unnecessary search paths. We evaluate the performance of our new method
on NFA/TA obtained from random regular expressions and from the intermediate
steps of regular model checking. The results show that our approach significantly
outperforms the previous antichain-based approach in most of the experiments.
1 Introduction
The language inclusion problem for regular languages is important in many application
domains, e.g., formal verification. Many verification problems can be formulated as a
language inclusion problem. For example, one may describe the actual behaviors of an
implementation in an automaton A and all of the behaviors permitted by the specifica-


Source: Abdulla, Parosh Aziz - Department of Information Technology, Uppsala Universitet


Collections: Computer Technologies and Information Sciences