U. Schoning and K.W. Wagner, "Collapsing Oracles, Census Functions, and Logarithmically Many Queries," Report No.140 (1987), Mathematics Institute, Univ. Augsburg.  Home/Search   Document Not in Database   Summary   Related Articles

.... TC) i.e. first order logic with ordering, plus a transitive closure operation, in which the transitive closure operator does not appear within any negation symbols [7] Now we have returned to the issue of complementation in the light of recent results on the collapse of the log space hierarchies [10, 2, 14]. We have shown that the class (FO pos TC) is closed under complementation. Our Research supported by NSF Grant DCR 8603346. main result follows. In this paper we give the proof in terms of machines and then state the result for transitive closure as Corollary 3. The question of whether (FO ....

....problems accepted by alternating log space Turing machines that make at most k Gamma 1 alternations and begin in an existential state. Recently Lange, Jenner, and Kirsig [10] showed that this hierarchy collapsed to the second level, Sigma 2 ALOG. This result was then extended by several authors [2, 14] who showed that the log space oracle hierarchy collapses to L NL . Here L=DSPACE[log n] and NL = NSPACE[log n] The logspace oracle hierarchy is given by Sigma 1 OLOG = NL, and Sigma k 1 OLOG = NL Sigma k OLOG . In the case of the polynomial time hierarchy, the oracle and alternating ....

U. Schoning and K.W. Wagner, "Collapsing Oracles, Census Functions, and Logarithmically Many Queries," Report No.140 (1987), Mathematics Institute, Univ. Augsburg.

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