Probabilistic quantifiers, adversaries, and complexity classes : An overview

  • Stathis Zachos
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 223)


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.


probabilistic algorithms complexity classes polynomial time quantifiers combinatorial games oracles and hierarchies 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Stathis Zachos
    • 1
  1. 1.Brooklyn College of CUNYNew York

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