 
Summary: Minimization of NonDeterministic Automata
with Large Alphabets #
Parosh Aziz Abdulla, Johann Deneux, Lisa Kaati, and Marcus Nilsson
Dept. of Information Technology, P.O. Box 337, S751 05 Uppsala, Sweden
{parosh,johannd,kaati,marcusn}@it.uu.se
Abstract. There has been several attempts over the years to solve the
bisimulation minimization problem for finite automata. One of the most
famous algorithms is the one suggested by Paige and Tarjan. The algo
rithm has a complexity of O(m log n) where m is the number of edges
and n is the number of states in the automaton. A bottleneck in the ap
plication of the algorithm is often the number of labels which may appear
on the edges of the automaton. In this paper we adapt the PaigeTarjan
algorithm to the case where the labels are symbolically represented using
Binary Decision Diagrams (BDDs). We show that our algorithm has an
overall complexity of O(# ˇ m ˇ log n) where # is the size of the alphabet.
This means that our algorithm will have the same worst case behavior as
other algorithms. However, as shown by our prototype implementation,
we get a vast improvement in performance due to the compact represen
tation provided by the BDDs.
1 Introduction
