Multipebble simulations for alternating automata

Authors:
Lorenzo Clemente;Richard Mayr
Affiliations:
LFCS, School of Informatics, University of Edinburgh, UK;LFCS, School of Informatics, University of Edinburgh, UK
Venue:
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Year:
2010

Citing 6
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Abstract

We study generalized simulation relations for alternating Büchi automata (ABA), as well as alternating finite automata. Having multiple pebbles allows the Duplicator to "hedge her bets" and delay decisions in the simulation game, thus yielding a coarser simulation relation. We define (k1, k2)-simulations, with k1/k2 pebbles on the left/right, respectively. This generalizes previous work on ordinary simulation (i.e., (1, 1)-simulation) for nondeterministic Büchi automata (NBA) in [4] and ABA in [5], and (1, k)-simulation for NBA in [3]. We consider direct, delayed and fair simulations. In each case, the (k1, k2)- simulations induce a complete lattice of simulations where (1, 1)- and (n, n)- simulations are the bottom and top element (if the automaton has n states), respectively, and the order is strict. For any fixed k1/k2, the (k1, k2)-simulation implies (ω-)language inclusion and can be computed in polynomial time. Furthermore, quotienting an ABA w.r.t. (1, n)-delayed simulation preserves its language. Finally, multipebble simulations yield new insights into theMiyano-Hayashi construction [10] on ABA. A technical report with full proofs is available [2].