Abstract
Several input read-modes for alternating Turing machines have been proposed in the literature. For each input read-mode and for each fixed integer k ≥ 1, a precise circuit characterization is established for log-time alternating Turing machines of k alternations, which is a nontrivial refinement of Ruzzo's circuit characterization of alternating Turing machines. Complete languages in strong sense for each level of the log-time hierarchy are presented, refining a result by Buss. The class GC(s(n), Π Bk ) is investigated, which is the class of languages accepted by log-time alternating Turing machines of k alternations enhanced by an extra ability of guessing a string of length s(n). A systematic technique is developed to show that for many functions s(n) and for every integer k>1, the class GC(s(n), Π Bk ) has natural complete languages. Connections of these results to computational optimization problems are exhibited.
Supported in part by Engineering Excellence Award from Texas A&M University.
Supported in part by the United States National Science Foundation grant CCR-9110824 and by a P.R.China HTP-863 grant.
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Cai, L., Chen, J. (1995). On log-time alternating Turing machines of alternation depth k . In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030843
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DOI: https://doi.org/10.1007/BFb0030843
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