Abstract
The concept of non-uniform proof systems is introduced. This notion allows a uniform description of non-uniform complexity classes [10], probabilistic classes (e.g. BPP [8,15,27,32], AM [2,3]) and language classes defined by simultaneous non-uniform and nondeterministic time bounds. Non-uniform proof systems provide a better understanding of many results concerning these classes, particularly their connections to uniform complexity measures. We give an uniform approach to lowness results [19,20] for various complexity classes. For instance, we show that co-NP/Poly ∩ NP is contained in the third level of the low hierarchy and that, NP c (NP ∩ co-NP)/Poly implies that the polynomial time hierarchy collapses to its second level (see also [1]). Finally, some evidence is given that the low hierarchy cannot be extended beyond its third level by the current techniques.
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Kämper, J. (1988). Non-uniform proof systems: A new framework to describe non-uniform and probabilistic complexity classes. In: Nori, K.V., Kumar, S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1988. Lecture Notes in Computer Science, vol 338. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50517-2_81
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DOI: https://doi.org/10.1007/3-540-50517-2_81
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