On communication-bounded synchronized alternating finite automata

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≥1L(SAFA(k-heads,nk -com)). This result recasts the relationships between P, NP, and PSPACE in terms of multihead synchronized alternating finite automata.