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- W1979916222 abstract "Unambiguity in alternating Turing machines has received considerable attention in the context of analyzing globally unique games by Aida et al. [ACRW] and in the design of efficient protocols involving globally unique games by Crasmaru et al. [CGRS]. This paper explores the power of unambiguity in alternating Turing machines in the following settings: 1. We show that unambiguity-based hierarchies-AUPH, UPH, and UPH-are infinite in some relativized world. For each $k geq 2$ , we construct another relativized world where the unambiguity-based hierarchies collapse so that they have exactly k distinct levels and their k-th levels coincide with PSPACE. These results shed light on the relativized power of the unambiguity-based hierarchies, and parallel the results known for the case of the polynomial hierarchy. 2. For every $k ge 1$ , we define the bounded-level unambiguous alternating solution class UAS(k) as the class of all sets L for which there exists a polynomial-time alternating Turing machine N, which need not be unambiguous on every input, with at most k alternations such that $xin L$ if and only if x is accepted unambiguously by N. We construct a relativized world where, for all $k geq 1, {rm UP}_{leq k} subset {rm UP}_{leq k+1}$ and ${rm UAS}(k) subset {rm UAS}(k+1)$ . 3. Finally, we show that robustly k-level unambiguous alternating polynomial-time Turing machines, i.e., polynomial-time alternating Turing machines that for every oracle have k alternating levels and are unambiguous, accept languages that are computable in ${rm P}^{Sigma^{p}_{k} oplus {cal A}}$ , for every oracle A. This generalizes a result of Hartmanis and Hemachandra [HH]." @default.
- W1979916222 created "2016-06-24" @default.
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- W1979916222 date "2007-08-01" @default.
- W1979916222 modified "2023-10-17" @default.
- W1979916222 title "On the Power of Unambiguity in Alternating Machines" @default.
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- W1979916222 doi "https://doi.org/10.1007/s00224-007-2014-y" @default.
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