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SIAM Journal on Computing
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Theoretical Computer Science
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CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
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POPL '13 Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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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.