Forward Bisimulations for Nondeterministic Symbolic Finite Automata

  • Loris D’Antoni
  • Margus VeanesEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10205)


Symbolic automata allow transitions to carry predicates over rich alphabet theories, such as linear arithmetic, and therefore extend classic automata to operate over infinite alphabets, such as the set of rational numbers. Existing automata algorithms rely on the alphabet being finite, and generalizing them to the symbolic setting is not a trivial task. In our earlier work, we proposed new techniques for minimizing deterministic symbolic automata and, in this paper, we generalize these techniques and study the foundational problem of computing forward bisimulations of nondeterministic symbolic finite automata. We propose three algorithms. Our first algorithm generalizes Moore’s algorithm for minimizing deterministic automata. Our second algorithm generalizes Hopcroft’s algorithm for minimizing deterministic automata. Since the first two algorithms have quadratic complexity in the number of states and transitions in the automaton, we propose a third algorithm that only requires a number of iterations that is linearithmic in the number of states and transitions at the cost of an exponential worst-case complexity in the number of distinct predicates appearing in the automaton. We implement our algorithms and evaluate them on 3,625 nondeterministic symbolic automata from real-world applications.


Greedy Algorithm Finite Automaton Binary Decision Diagram Finite Alphabet Deterministic Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Loris D’Antoni performed part of this work while visiting Microsoft Research, Redmond. We thank Zachary Kincaid for his feedback.


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.University of WisconsinMadisonUSA
  2. 2.Microsoft ResearchRedmondUSA

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