Büchi Automata Can Have Smaller Quotients

  • Lorenzo Clemente
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6756)


We study novel simulation-like preorders for quotienting nondeterministic Büchi automata. We define fixed-word delayed simulation, a new preorder coarser than delayed simulation. We argue that fixed-word simulation is the coarsest forward simulation-like preorder which can be used for quotienting Büchi automata, thus improving our understanding of the limits of quotienting. Also, we show that computing fixed-word simulation is PSPACE-complete.

On the practical side, we introduce proxy simulations, which are novel polynomial-time computable preorders sound for quotienting. In particular, delayed proxy simulation induce quotients that can be smaller by an arbitrarily large factor than direct backward simulation. We derive proxy simulations as the product of a theory of refinement transformers: A refinement transformer maps preorders nondecreasingly, preserving certain properties. We study under which general conditions refinement transformers are sound for quotienting.


Direct Simulation Forward Simulation Input Word Simulation Game 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.


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lorenzo Clemente
    • 1
  1. 1.LFCS, School of InformaticsUniversity of EdinburghUK

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