A Protocol for Serializing Unique Strategies

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.