Abstract
We consider inclusion relations among a multitude of classical complexity classes and classes with probabilistic components. A key tool is a method for characterizing such classes in terms of the ordinary quantifiers ∃ and ∀ together with a quantifier ∃+, which means roughly “for most”, applied to polynomial-time predicates. This approach yields a uniform treatment which leads to easier proofs for class-inclusion and hierarchy-collapse results. Furthermore the method captures some recently introduced game classes and game hierarchies.
This survey also includes a charting of class-inclusion and oracle-based separation results.
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© 1986 Springer-Verlag Berlin Heidelberg
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Zachos, S. (1986). Probabilistic quantifiers, adversaries, and complexity classes : An overview. In: Selman, A.L. (eds) Structure in Complexity Theory. Lecture Notes in Computer Science, vol 223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16486-3_112
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DOI: https://doi.org/10.1007/3-540-16486-3_112
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