Multipebble Simulations for Alternating Automata-( Extended 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 decision s 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 pr vious work on ordinary simulation (i.e., (1, 1)-simulation) for nondeterministic Büchi automata (NBA) in [3] and ABA in [4], and(1, k)-simulation for NBA in [2]. We consider direct, delayed and fair simulations. In each ca se, 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 hasn 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 t he Miyano-Hayashi construction [10] on ABA.