DSPACE[nk] = VAR[k+1]
نویسنده
چکیده
In this paper we prove that the set of properties check-able by a Turing machine in DSPACEn k ] is exactly equal to the set of properties describable by a uniform sequence of rst-order sentences using at most k + 1 distinct variables. We prove that this is also equal to the set of properties describable using an iterative definition for a nite set of relations of arity k. This is a reenement of the theorem PSPACE = VARRO1]] I82]. We suggest some directions for exploiting this result to derive trade-oos between the number of variables and the quantiier-depth in desciptive complexity. This has applications to parallel complexity.
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