Abstract
We continue the study of communication-bounded synchronized alternating finite automata (SAFA), first considered by Hromkovič et al. We show that to accept a nonregular language, an SAFA needs to generate at least Ω(log logn) communication symbols infinitely often; furthermore, a synchronized alternating finite automaton without nondeterminism (SUFA) needs to generate at leastΩ(log logn) communication symbols infinitely often for some constantk≥1. We also show that these bounds are tight.
Next, we establish dense hierarchies of these machines on the function bounding the number of communication symbols. Finally, we give a characterization of NP in terms of communication-bounded multihead synchronized alternating finite automata, namely, NP = ⋃ k≥1 L(SAFA(k-heads,n k -com)). This result recasts the relationships between P, NP, and PSPACE in terms of multihead synchronized alternating finite automata.
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Research supported in part by NSF Grant CCR89-18409
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Ibarra, O.H., Tran, N.Q. On communication-bounded synchronized alternating finite automata. Acta Informatica 31, 315–327 (1994). https://doi.org/10.1007/BF01178509
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DOI: https://doi.org/10.1007/BF01178509