Abstract
We devise an efficient protocol by which a series of two-person games G i with unique winning strategies can be combined into a single game G with unique winning strategy, even when the result of G is a non-monotone function of the results of the G i that is unknown to the players. In computational complexity terms, we show that the class UAP of Niedermeier and Rossmanith [10] of languages accepted by unambiguous polynomial-time alternating TMs is self-low, i.e., \({\rm UAP}^{\ rm UAP} = {\rm UAP}\). It follows that UAP contains the Graph Isomorphism problem, nominally improving the problem’s classification into SPP by Arvind and Kurur [2] since UAP is a subclass of SPP [10]. We give some other applications, oracle separations, and results on problems related to unique-alternation formulas.
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Crasmaru, M., Glaßer, C., Regan, K.W., Sengupta, S. (2004). A Protocol for Serializing Unique Strategies. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_51
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DOI: https://doi.org/10.1007/978-3-540-28629-5_51
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