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Deterministic versus nondeterministic space in terms of synchronized alternating machines. (English) Zbl 0821.68056
Summary: The study of synchronized alternating machines has enabled to characterize several natural complexity classes. It is known that synchronized alternating space $$\text{SASPACE}(S(n)) = \bigcup_{c > 0} \text{NSPACE}(nc^{S(n)})$$ for any (space-constructible) function $$S(n)$$. In particular, context-sensitive languages are characterized by two-way synchronized alternating finite automata. Furthermore, PSPACE is characterized by synchronized alternating multihead finite automata. Furthermore, PSPACE is characterized by synchronized alternating multihead finite automata and NLOG by synchronized alternating two-way finite automata with parallelism bounded by a constant. In the present paper we prove analogous characterizations for deterministic space classes using a restricted form of synchronization – globally deterministic synchronization. This enables to study the well-known open problems concerning nondeterminism versus determinism as problems about synchronization. We also show that globally deterministic synchronization is strictly more powerful than deterministic synchronization.

##### MSC:
 68Q15 Complexity classes (hierarchies, relations among complexity classes, etc.) 03D15 Complexity of computation (including implicit computational complexity)
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##### References:
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